Question

The question just asks “Find QT” pls help

Answer 1

QT = 21

Explanation:

Because the left section is technically just a extension of the right triangle, the two triangles (PRQ and SRT) are similar, so the ratio between the sides will be similar as well.

The small triangle (SRT) has a ratio of 8/7 between its top side SR (40) and its bottom side TR (35). This means that the top and bottom side of the triangle PRQ will have the same ratio, and since we already known PR (24+40), we can write an equation to solve for QR:

`(SR)/(TR) =(PR)/(QR) \\\\\\frac{40}{35}=(64)/(?)`

`(8)/(7) =(64)/(?)`

64/8=8

This means so get our unknow length, we will need to multiply 7 by 8.

7*8=56

`(8)/(7) =(64)/(56)`

This means that the side QR is 56, and since we know TR is 35, we simply need to subtract 35 from 56 to find QT: 56-35= 21

PS and QT also have the same ratio: 24/21 = 8/7 so we know that this is correct.

Hope this helped!