A rectangle is 3 times as long as it is wide and has the sam

A rectangle is 3 times as long as it is wide and has the same perimeter as a square whose area is 25 square feet larger than the area of the rectangle. What are the dimensions of the rectangle?

Solution

solution -: Let the width be x

the length will be 3x

so the the perimeter of rectangle = 2*x+2*3x =8x

rectangle:
width = x
length = 3x
perimeter = 8x
area = 3x^2

square:
side y
perimeter = 4y
area = y^2

perimeters are the same --> 4y = 8x
y = 2x

area of square is 25 more than area of rectangle

y^2 = 3x^2 + 25
4x^2 = 3x^2 + 25
x^2 = 25
x = 5, then y = 10

rectangle:
width = 5
length = 15
perimeter = 40
area = 75

square:
side = 10
perimeter = 40
area =100 , which is 25 more than that of the rectangle