Help Solve The Form 1 Math Question

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Introduction

Mathematics is a fundamental subject that plays a crucial role in our daily lives. It is a subject that requires problem-solving skills, logical thinking, and analytical reasoning. In Form 1, students are introduced to various mathematical concepts, including geometry, algebra, and trigonometry. One of the key areas of focus in Form 1 is metric geometry, which deals with the study of shapes, sizes, and positions of objects. In this article, we will help solve a Form 1 math question related to metric geometry, specifically finding the length of DE.

Understanding the Graph

To find the length of DE, we need to understand the given graph. The graph shows a rectangle with points A, B, C, and D marked on it. The length of AB is 6 cm, and the length of BC is 8 cm. We are asked to find the length of DE.

Using the Pythagorean Theorem

To find the length of DE, we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In this case, we can use the Pythagorean theorem to find the length of DE.

Step 1: Identify the Right-Angled Triangle

To apply the Pythagorean theorem, we need to identify the right-angled triangle in the graph. Looking at the graph, we can see that triangle ADE is a right-angled triangle, with angle ADE being the right angle.

Step 2: Apply the Pythagorean Theorem

Now that we have identified the right-angled triangle, we can apply the Pythagorean theorem to find the length of DE. The Pythagorean theorem states that:

a^2 + b^2 = c^2

where a and b are the lengths of the two sides that form the right angle, and c is the length of the hypotenuse (DE in this case).

Step 3: Plug in the Values

We know that the length of AB is 6 cm, and the length of BC is 8 cm. We can use these values to plug into the Pythagorean theorem equation.

a = 6 cm (length of AB) b = 8 cm (length of BC) c = DE (length of DE)

Step 4: Solve for DE

Now that we have plugged in the values, we can solve for DE.

6^2 + 8^2 = DE^2 36 + 64 = DE^2 100 = DE^2

Step 5: Find the Length of DE

To find the length of DE, we need to take the square root of both sides of the equation.

DE = √100 DE = 10 cm

Conclusion

In this article, we helped solve a Form 1 math question related to metric geometry, specifically finding the length of DE. We used the Pythagorean theorem to find the length of DE, and we were able to arrive at the correct answer of 10 cm. This problem-solving exercise demonstrates the importance of understanding mathematical concepts and applying them to real-world problems.

Additional Tips and Tricks

  • When solving math problems, it's essential to read the question carefully and understand what is being asked.
  • Use diagrams and graphs to visualize the problem and identify the key elements.
  • Apply mathematical concepts and formulas to solve the problem.
  • Check your work and make sure that your answer is reasonable and makes sense in the context of the problem.

Frequently Asked Questions

  • Q: What is the Pythagorean theorem? A: The Pythagorean theorem is a mathematical concept that states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
  • Q: How do I apply the Pythagorean theorem to find the length of DE? A: To apply the Pythagorean theorem, you need to identify the right-angled triangle, plug in the values, and solve for DE.
  • Q: What is the length of DE? A: The length of DE is 10 cm.

Related Topics

  • Metric geometry
  • Pythagorean theorem
  • Right-angled triangles
  • Math problem-solving skills

References

Introduction

In our previous article, we helped solve a Form 1 math question related to metric geometry, specifically finding the length of DE. We used the Pythagorean theorem to find the length of DE, and we were able to arrive at the correct answer of 10 cm. In this article, we will provide a Q&A section to help students better understand the concept and answer any questions they may have.

Q&A Section

Q: What is the Pythagorean theorem?

A: The Pythagorean theorem is a mathematical concept that states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

Q: How do I apply the Pythagorean theorem to find the length of DE?

A: To apply the Pythagorean theorem, you need to identify the right-angled triangle, plug in the values, and solve for DE. In this case, we used the Pythagorean theorem to find the length of DE, and we were able to arrive at the correct answer of 10 cm.

Q: What is the formula for the Pythagorean theorem?

A: The formula for the Pythagorean theorem is:

a^2 + b^2 = c^2

where a and b are the lengths of the two sides that form the right angle, and c is the length of the hypotenuse (DE in this case).

Q: How do I identify a right-angled triangle?

A: To identify a right-angled triangle, you need to look for a triangle with one angle that is 90 degrees. In this case, we identified triangle ADE as a right-angled triangle, with angle ADE being the right angle.

Q: What is the length of DE?

A: The length of DE is 10 cm.

Q: Can I use the Pythagorean theorem to find the length of other sides of a triangle?

A: Yes, you can use the Pythagorean theorem to find the length of other sides of a triangle. However, you need to make sure that the triangle is a right-angled triangle, and that you have the correct values for the other two sides.

Q: What if I get a negative answer when using the Pythagorean theorem?

A: If you get a negative answer when using the Pythagorean theorem, it means that the triangle is not a right-angled triangle, or that you have made an error in your calculations.

Q: Can I use the Pythagorean theorem to find the length of a side of a triangle that is not a right-angled triangle?

A: No, you cannot use the Pythagorean theorem to find the length of a side of a triangle that is not a right-angled triangle. The Pythagorean theorem only applies to right-angled triangles.

Additional Tips and Tricks

  • When solving math problems, it's essential to read the question carefully and understand what is being asked.
  • Use diagrams and graphs to visualize the problem and identify the key elements.
  • Apply mathematical concepts and formulas to solve the problem.
  • Check your work and make sure that your answer is reasonable and makes sense in the context of the problem.

Frequently Asked Questions

  • Q: What is the Pythagorean theorem? A: The Pythagorean theorem is a mathematical concept that states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
  • Q: How do I apply the Pythagorean theorem to find the length of DE? A: To apply the Pythagorean theorem, you need to identify the right-angled triangle, plug in the values, and solve for DE.
  • Q: What is the length of DE? A: The length of DE is 10 cm.

Related Topics

  • Metric geometry
  • Pythagorean theorem
  • Right-angled triangles
  • Math problem-solving skills

References