Need some help with this. It says to find x.

Question

asked Feb 13, 2023 48.3k views

2 Answers

Kittycatbytes · Answer 1 · 2023-02-17T16:18:36+0000

Answer:

x= 5

Explanation:

Since RQ= PQ,

3x= 15

Divide both sides by 3:

x= 15 ÷3

$\textcolor{red}{x = 5}$

$\textcolor{steelblue}{\text{Prove for RQ}= \text{PQ}}$

Let SP= x

RS= SP= x (given)

Let SQ= y

Applying Pythagoras' Theorem,

In triangle QRS

(RQ)²= (RS)² +(SQ)²

(RQ)²= x² +y²

$RQ = \sqrt{ {x}^(2) + {y}^(2) }$

In triangle QPS

(PQ)²= (SP)² +(SQ)²

(PQ)²= x² +y²

$PQ = \sqrt{ {x}^(2) + {y}^(2) }$

Thus, RQ= PQ.