Question

Enlargements question- 20 POINTS :)

Answer 1

x = 6.5

Explanation:

Δ TPS and Δ QPR are similar ( AA postulate ) , so the ratios of corresponding sides are in proportion, that is

`(PS)/(PR)` =
`(TS)/(QR)` ( substitute values )

`(x)/(x+2.6)` =
`(5)/(7)` ( cross- multiply )

7x = 5(x + 2.6) ← distribute parenthesis

7x = 5x + 13 ( subtract 5x from both sides )

2x = 13 ( divide both sides by 2 )

x = 6.5

Answer 2

x = 6.5 cm

Explanation:

make a equation to solve enlargements:

ST = 5 cm, QR = 7 cm, PS = x cm, PR = x + 2.6 cm

`(x)/(5) = (x+2.6)/(7)`

7(x) = 5(x+2.6)

7x = 5x + 13

7x - 5x = 13

2x = 13

x = 6.5 cm