Question

What is the length of line PS

Answer 1

`PQ^2 = PR * PS`


`(4x + 4)^2 = (3x + 3)(3x + 3 + 21)`


`16x^2 + 32x + 16= (3x + 3)(3x + 24)`


`16x^2 + 32x + 16= 9x^2 + 81x + 72`


`7x^2 - 49x- 56 = 0`


`7(x^2 - 7x - 8)= 0`


`(x - 8)(x + 1) = 0`


`x - 8 = 0~~~or~~~x + 1 = 0`


`x = 8~~~or~~~x = -1`

x = -1 makes the lengths of segments PQ and PR equal zero.
That is not possible, so the solution x = -1 is discarded.

x = 8

PS = 3x + 3 + 21

PS = 3x + 24

PS = 3(8) + 24

PS = 24 + 24

PS = 48