Question

The right triangle shown below is formed by joining three squares at their vertices. What is the value of x , the side length of the smallest square?

Answer 1

To find the value of x, use the Pythagorean theorem. The equation x^2 + x^2 = 8^2 can be simplified to 2x^2 = 64. The solution is x = 4√2 inches.

Step-by-step explanation:

To find the value of x, we need to use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In this case, the hypotenuse is the side length of the largest square and is equal to 8 inches (twice the side length of the smallest square). So the equation becomes: x^2 + x^2 = 8^2.

Simplifying the equation, we have: 2x^2 = 64. Dividing both sides by 2, we get: x^2 = 32. Taking the square root of both sides, we find: x = √32 = 4√2 inches.

Answer 2

B: 8

Step-by-step explanation:

The area of the two smaller squares equals the area of the big square so find the area to the big square

17 * 17 = 289

289 - 225 = 64

The square root of 64 is 8 so the answer is 8.