Solving for side of square given diagonal

Can someone correct me?

Problem: The diagonal of a square quilt is 4 times the square root of 2. What is the area of the quilt in square feet?

The answer is 4. My book suggests that we use the property of a 45 45 90 triangle to solve this. I understand that method. However, I initially attempted to solve it by using Pythagorean theorem with the diagonal being the hypotenuse. I came up with 4 x 2^(1/2) = 2 x (a^2) I proceeded to divide the left side by 2, and I did not come up with 4 for the answer. Why is this?

Re: Solving for side of square given diagonal

If you want to use Phytagoras then, let $\displaystyle a$ be the side of the square quilt therefore:

$\displaystyle a^2+a^2=(4\sqrt{2})^2$

Solve this equation for $\displaystyle a$.

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Re: Solving for side of square given diagonal

Quote:

Originally Posted by

**benny92000** Can someone correct me?

Problem: The diagonal of a square quilt is 4 times the square root of 2. What is the **area of the quilt** in square feet?

The answer is 4. **<--- That is the side-length and not the area**

My book suggests that we use the property of a 45 45 90 triangle to solve this. I understand that method. However, I initially attempted to solve it by using Pythagorean theorem with the diagonal being the hypotenuse. I came up with 4 x 2^(1/2) = 2 x (a^2) I proceeded to divide the left side by 2, and I did not come up with 4 for the answer. Why is this?

1. Draw a sketch.

2. The quilt is placed inside a square of the side-length d.

3. You can prove (by congruent triangles) that the **area of the quilt** is

$\displaystyle A = \frac12 \cdot d^2$

4. Plug in the value for d and you'll get the given result.

5. If you want to calculate the side-length then $\displaystyle a = \sqrt{A}=d \cdot \sqrt{\frac12}$

Re: Solving for side of square given diagonal

Siron has calculated the sides of the square when what was asked for was the area, s^2.

Re: Solving for side of square given diagonal

Quote:

Originally Posted by

**cathectio** Siron has calculated the sides of the square when what was asked for was the area, s^2.

no kidding ...

**Siron** most probably assumed the OP was capable of determining the area of a square once he/she determined the side length.

Effective tutoring sometimes requires providing just enough information to let the OP solve the problem (or screw it up) on their own.