Question

Perimeter of a rectangle is 4 cm more than 2/3 of the perimeter of a square if the perimeter of the square is 84 cm find the length and breadth of the rectangle given that the breadth is 1/4 of the le ngth

Answer 1

Given Data.
perimeter of rectangle = 4 + 2/3(perimeter of square)
perimeter of rectangle = 2(length + width)
perimeter of square = 4( side length)
from the given perimeter of square = 84 cm
p(s) = perimeter of square
p(r) = perimeter of rectangle

so p(s) = 84
4* side = 84
side = 21 cm

from the question
p(r) = 4+2/3 ( p(s))
p(r) = 4 + 2/3 (84)
p(r) = 4 + 2( 28)
p(r) = 4+56
p(r) = 60 cm

given breadth = 1/4 (length)
so length = 4breadth

p(r) = 60
2(l+b) = 60
2( 4b+b) = 60
2(5b) = 60
10b = 60
divide with 10 on both sides
b = 6 cm .

so length = 4*breadth
length = 4*6= 24 cm

so length and breadth of a rectangle are 24cm and 6cm respectively


Hope it helps!