Question

PQRS is a rectangle such that PR+PQ=5PS and PR-PS=8. then area of rectangle is

Answer 1

Answer:

60 sq units

Step-by-step explanation:

Let say PQ = RS = L  (length of rectangle)

QR = PS = B  ( breadth of rectangle)

PR = √(PQ² + QR²)    = √(L² + B²)    (Diagonal of rectangle)

PR  + PQ  = 5 PS

√(L² + B²) + L = 5B

=> √(L² + B²) = 5B - L

PR - PS = 8

=> √(L² + B²)  - B = 8

=> √(L² + B²)  = 8 + B

Equating √(L² + B²)  

5B - L = 8 + B

=> 4B - L = 8

=> L = 4B - 8

=> √((4B - 8)² + B²)  = 8 + B

Squaring both side

16B² + 64 - 64B  + B² = 64 + B² + 16B

=> 16B² - 80B  = 0

=> 16B(B - 5) = 0

=> B = 5   ( as Breadth can not be Zero)

L = 4*5 - 8  = 12

Area = LB = 12 * 5 = 60 sq units