Question

the perimeter of a rectangle is 44 m. If the width were doubled and the length were increased by 8 m, the perimeter would be 76 m. What is the length of the rectangle

Answer 1

Let us assume the length of the first rectangle = x meter
let us assume the width of the first rectangle = y meter
Perimeter of the first rectangle = 44 meter
we already know
Perimeter of a rectangle = 2 (Length + Width)
Then in the case of the first rectangle we get
44 = 2(x + y)
44/2 = x + y
x + y = 22
y = 22 - x
Now coming to the case of the second rectangle
The length of the second rectangle = x + 8
The width of the second rectangle = 2y
Perimeter of the second rectangle = 76 meter
then
76 = 2[(x + 8) + 2y]
76/2 = x + 8 + 2y
38 = x + 2y + 8
x + 2y = 38 - 8
x + 2y = 30
Now we replace the value of y that we found from the first equation. Then
x + 2(22 - x) = 30
x - 2x + 44 = 30
-x = 30 - 44
-x = -14
x = 14
So the length of the first rectangle is 14 meters.