Question

The length of a rectangle is 5 cm, and the width is 4 cm. If both the length and the width are increased by equal amounts, the are of the rectangle is increased by 70 cm2. Find the length and width of the longer rectangle.

Answer 1

Length = 10cm, Width = 9 cm

Explanation:

Let's call the amount that both the length and width are increased by "x". So, the new length is 5 + x and the new width is 4 + x.

The original area of the rectangle was 5 * 4 = 20 cm2.

The new area of the rectangle after the increase is (5 + x) * (4 + x) = 20 + 70 + 2x^2.

Expanding the right-hand side, we have 20 + 70 + 2x^2 = 90 + 2x^2.

Equating the two areas, we get:

20 + 70 + 2x^2 = 90 + 2x^2

Subtracting 2x^2 from both sides:

20 + 70 = 90

Subtracting 20 from both sides:

70 = 70

So x^2 = 50 / 2 = 25.

Taking the square root of both sides, we get:

x = 5

So the length of the longer rectangle is 5 + x = 5 + 5 = 10 cm, and the width is 4 + x = 4 + 5 = 9 cm.