Question

(Will give brainlist) What is the value of x? This figure is not drawn to scale.
- $\sqrt{143}$
- 143
-24
- $\sqrt{24}$

Answer 1

Answer:

$x = \sqrt{143}$

Step-by-step explanation:

We know that all three triangles formed by dropping a right triangle's altitude (here labeled $x$) are similar.

This means that the ratios of their side lengths are equal. We can use this property to solve for $x$:

$\dfrac{\text{short leg of small }\triangle }{\text{long leg of small }\triangle} = \dfrac{\text{short leg of medium }\triangle }{\text{long leg of medium }\triangle}$

↓ plugging in the given values

$\dfrac{11}{x} = \dfrac{x}{13}$

↓ cross-multiplying

$x^2 = 11 \cdot 13$

↓ taking the square root of both sides

$\boxed{x = \sqrt{143}}$