Question

The length of the diagonal of a rectangle is 10cm. If the length is 2cm longer than the width, find the length and the width of the rectangle.

Answer 1

Answer:

the length and the width of the rectangle is 8 cm and 6 cm respectively.

Step-by-step explanation:

Given the diagonal length of the rectangle, we can use Pythagorean theorem to get the width and the length.

Now, let the width of the rectangle be x.

The length = x + 10

According to Pythagorean theorem:

10² = x² + (x + 2)²

100 = x² + x² + 4x + 4

100 = 2x² + 4x + 4

Divide through by 2:

50 = x² + 2x + 2

x² + 2x - 48 = 0

Let's solve for x as follows:

x² + 8x - 6x - 48 = 0

x(x + 8) - 6( x + 8) = 0

(x - 6)(x + 8) = 0

x = 6 or -8

We take the positive value. So, x = 6 cm

The width of the rectangle = 6 cm

The length = 6 + 2 = 8 cm