Question

Area of a square is 4sq.m more than 2/3 of the area of the rectangle.If the area of the square is 64 sq.m then find the dimension of the rectangle ,given that breadth is 2/5 of length.

Answer 1

Let the length of rectangle be X,
Now,
Breadth = 2/5x.
Area of rectangle =l*b
=x*2/5x=2x^2/5.
So,
Area of square = 4+2/3*2x^2/5
64x^2/15=64
x=√15m^2.
Now,
length =√15m
breadth =2/5*√15
=2√15/5m.
hope you have got it..

Answer 2

let area of the square S=64sq. m
let area of rectangle A=length L x breadt B
breadt B=2/5 L...............1)
form question,
S=4+2/3A
64=4+2/3 LxB
64=4+(2x2/5x3)L^2
4/15L=60
L^2=15x60/4
L=15m
putting the value of L in equation 1 we have,
B=2/5L
B=2x15/5
B=6m
hence, the dimension of the rectangle are 15m and 6m respectively.