Question

find the unknown side length, x. write your answer in simplest radical form.
a. 24
b. $4\sqrt{37}$
c. $2\sqrt{154}$
d. $5\sqrt{117}$

Explanation:

Step1: Find height of large triangle

Let height = $h$. Use Pythagoras:
$$h^2 + 7^2 = 25^2$$
$$h^2 = 25^2 - 7^2 = 625 - 49 = 576$$
$$h = \sqrt{576} = 24$$

Step2: Find base for triangle with side $x$

Base length = $7 - 3 = 4$

Step3: Solve for $x$ with Pythagoras

$$x^2 = h^2 + 4^2$$
$$x^2 = 24^2 + 4^2 = 576 + 16 = 592$$
$$x = \sqrt{592} = \sqrt{16 \times 37} = 4\sqrt{37}$$

Answer:

B. $4\sqrt{37}$