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

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 =
`(1.25B^(2) )/(L_(s) ^(2))`

referring to equ 1

ratio of area of recatngle to square =
`(1.25* (0.889L_(s)) ^(2) )/(L_(s) ^(2))`

=
`( 0.9879L_(s) ^(2) )/(L_(s) ^(2))`

ratio of area of recatngle to square= 0.9879