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

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.