Question

ABCD and PQRS are similar figures. AB= 12cm, BC=x cm, CD= 15 cm, AD= 10 cm, PQ= 8 cm, QR = 5 cm, RS = m cm and PS = n cm .Find the values of x, m and n. 

Answer 1

Given : quadrilateral ABCD ∼ quadrilateral PQRS

To find : x , m and n

Sol : quadrilateral ABCD ∼ quadrilateral PQRS

`"AB"/"PQ" = "BC"/"QR" = "DC"/"SR" = "AD"/"SR"`

`12/8 = "x"/5 = 15/"m" = 10/"n"`

`12/8 = "x"/5 , 12/8 = 15/"m" , 12/8 = 10/"n"`

60 = 8x , 4 m = 40 , 3n = 20

x = `60/8` , m = 10 cm , n = `20/3`

x = `15/2`  , m = 10 cm , n = 6.66...

x = 7.5 cm , m = 10 cm  , n = 6.67 cm