Question

If the length of a rectangle is decreased by 4 cm and the width is increased by 5 cm, the result will be a square, the area of which will be 40 cm2 greater than the area of the rectangle. Find the area of the rectangle.

Answer 1

Answer:

If the length of a certain rectangle is decreased by 4 cm and the width is increased by 3 cm, a square with the same area as the original rectangle would result. Find the perimeter of the original rectangle.

Let us assume the length and width of the rectangle are L and W, respectively, in cm.

Now, length of the square is (L - 4) cm and width of the square is (W + 3)

And, as it is a square, length = width ---> (L - 4) = (w + 3) ---> L = W + 7

So, area of the square = (L - 4)(W + 3) = (W + 3)²

And, area of the rectangle = LW = (W + 7)W

So, (W + 3)² = (W + 7)W

--> W² + 6W + 9 = W² + 7W

--> W = 9

--> L = (9 + 7) = 16

So, the perimeter of the rectangle = 2*(L + W) = 2*(16 + 9) = 2*25 = 50

Answer 2

answerat be 50

Hope it helps you friends