Question

Need help with similarity here

Answer 1

see explanation

Explanation:

Since the figures are similar then the ratios of corresponding sides are in proportion.

(a)

`(PQ)/(AB)` =
`(RS)/(CD)` ( substitute values )

`(PQ)/(6)` =
`(12)/(8)` ( cross- multiply )

8 × PQ = 72 ( divide both sides by 8 )

PQ = 9 cm

(b)

`(AD)/(PS)` =
`(CD)/(RS)` ( substitute values )

`(AD)/(10.5)` =
`(8)/(12)` ( cross- multiply )

12 × AD = 84 ( divide both sides by 12 )

AD = 7 cm

(c)

given 2 similar figures with ratio of sides = a : b , then

ratio of areas = a² : b²

here ratio of sides CD : RS = 8 : 12 = 2 : 3

then ratio of areas = 2² : 3² = 4 : 9

let the area of PQRS be x , then using proportion

`(4)/(48)` =
`(9)/(x)` ( cross- multiply )

4x = 432 ( divide both sides by 4 )

x = 108

then area of PQRS = 108 cm²