Question

If the perimeter of a rectangle and a square, each is equal to 80 cm and the difference of their areas is 100 sq. cm, the sides of the rectangle ar

Answer 1

the perimeter of the square is 80, then each side is 80/4, or 20.
That makes the area of the square 20*20=400
Since the difference between the rectangle and the square are is 100, the area of the rectangle equals either 500 or 300.
They're even numbers, so we'll assume that the sides are even, too.
2L + 2W = 80, therefore L + W = 40
We're looking for factors of 500 (or 300; we'll do that next if 500 doesn't work) that equal 40 when added.
Factors of 500:
1 and 500 = 501
2 and 250 =252
4 and 125 = 129
5 and 100 = 105
10 and 50 = 60

20 and 25 = 45
None of the factors of 500 fit the scenario. Let's try the other possibility, 300
Factors of 300:
1 and 300 = 301
2 and 150 = 152
3 and 100 = 103
4 and 75 = 79
5 and 60 = 65
6 and 50 = 56
10 and 30 = 40 
12 and 25 = 37
15 and 20 = 35

Answer 2

area of rectangle= l×b
area of square= a^2
if l=30 & b= 10 then perimeter of rectangle is (30+10)×2=80
and if a= 20 then perimetre of square is 4×20=80
hence area of square is 20×20= 400
and area of rectangle is 30×10=300 and the diff. of area is 100

thus the sides of rectangle are 30, 10, 30, 10
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