Question

A rectangle and a square have the same perimeter. One side-length of the rectangle is $25\%$ longer than the other. What is the ratio between the areas of the rectangle and the square?

Answer 1

corrected question:

A rectangle and a square have the same perimeter. One side-length of the rectangle is 25% longer than the other. What is the ratio between the areas of the rectangle and the square?

Answer:

ratio of area of recatngle to square= 0.9879

Step-by-step explanation:

perimeter of rectangle = 2(L+B)

perimeter of a square =$4L_(s)$

L=B+0.25B

L=1.25B

$4L_(s)$= 2(L+B)

$4L_(s)$= 2(1.25B+B)

$4L_(s)$= 2(2.25B)

$4L_(s)$= 4.5B

B= 4/4.5 $L_(s)$

B= 0.889 $L_(s)$       ..........equ1

area of square =$L_(s)^{2}$

area of rectangle = L*B

                           =1.25B*B=$1.25B^{2}$

ratio of area of recatngle to square =$\frac{1.25B^{2} }{L_{s} ^{2}}$

referring to equ 1

ratio of area of recatngle to square = $\frac{1.25* (0.889L_{s}) ^{2} }{L_{s} ^{2}}$

=$\frac{ 0.9879L_{s} ^{2} }{L_{s} ^{2}}$

ratio of area of recatngle to square= 0.9879