Question

find the value of ( x ). leave your answer in simplest radical form.
image of a geometric figure: a right triangle with legs 6 and 6 on top of a rectangle. the rectangle has a diagonal of 10, and one side is labeled ( x ).
answer
attempt 1 out of 2
( x = ) input box submit answer
square root button

Explanation:

Step1: Find base of the triangle

Use Pythagorean theorem for the right triangle:
$$c^2 = a^2 + b^2$$
Let the base be $b$, so:
$$b^2 = 6^2 + 6^2 = 36 + 36 = 72$$
$$b = \sqrt{72} = 6\sqrt{2}$$

Step2: Find $x$ using rectangle diagonal

The base of the triangle equals the length of the rectangle. Use Pythagorean theorem for the rectangle's right triangle (with diagonal 10):
$$x^2 + (6\sqrt{2})^2 = 10^2$$
$$x^2 + 72 = 100$$
$$x^2 = 100 - 72 = 28$$
$$x = \sqrt{28} = 2\sqrt{7}$$

Answer:

$2\sqrt{7}$