The perimeter of the rectangle is 90. If the base of the rectangle is increased by 30 and the height is decreased

| July 15, 2021 | education

The perimeter of the rectangle is 90. If the base of the rectangle is increased by 30 and the height is decreased by 20, then the resulting rectangle will have the same area as the original. Find the sides of the original rectangle.

1. The perimeter of the rectangle is 90.

So the sum of the base and the height is 90/2 = 45.

2. Let X be the base of the rectangle.

Then (45 – X) is the height of the rectangle.

X * (45 – X) – area of ​​the rectangle.

3. (X + 30) – the new base of the rectangle.

(45 – X – 20) is the new height of the rectangle.

(X + 30) * (45 – X – 20) – new area.

4. By condition, the new area is equal to the area of ​​the original rectangle.

We got the equation.

X * (45 – X) = (X + 30) * (45 – X – 20).

45 * X – X * X = (X + 30) * (25 – X).

45 * X – X * X = 25 * X – X * X + 30 * 25 – X * 30.

45 * X – 25 * X + 30 * X = 750.

50 * X = 750.

X = 750/50.

X = 15.

This is the base of the original rectangle.

Let’s find the height.

45 – X = 45 – 15 = 30.

Answer: The sides of the original rectangle are 15 and 30.



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