Question

If triangle PQR is similar to SQT, find the value of

PQ.
X-9
S
T
8
Y +5
P
R
21
X = 15
PQ = 26

Answer 1

x = 15, PQ = 26

Explanation:

x+13/9 = 21/x-9

x^2+4x−117=168

x^2+4x−285=0

(x−15)(x+19)=0

x=15

it cannot be a negative number so x cannot be -19

PQ= x+13

15+13=26

Answer 2

x = 31.4

PQ = 58.8

Explanation:

Set up a proportion:

SQ/QP = ST/PR

Substitute in the values they give you:

`(x-9)/(x-9+x+5) = (8)/(21)`

`(x - 9)/(2x - 4) = (8)/(21)`

`21x - 189 = 16x - 32\\5x = 157\\x = 31.4`

This means that PQ = 2x - 4 = 2(31.4) - 4 = 62.8-4 = 58.8