# The width of a rectangle is 6 feet, and the diagonal is 10 feet. What is the area of the rectangle?

**Solution:**

We will use pythagorean theorem to find the length of the rectangle and then use the formula of area of rectangle.

Let ABCD be the rectangle and BD is the diagonal.

<<Remove heading deduction of diagonal of rectangle formula>>

Given that the length of the diagonal is 10 ft and width of the rectangle is 6 ft.

Using pythagorean theorem in triangle ABD

d^{2} = l^{2} + w^{2}

(10)^{2} = l^{2} + (6)^{2}

l^{2} = 100 - 36

l^{2} = 64

Take square root on both sides.

l = 8 ft

By using the formula of area of rectangle, we get

Area of rectangle = length × width

= 8 × 6

= 48 sq ft.

## The width of a rectangle is 6 feet, and the diagonal is 10 feet. What is the area of the rectangle?

**Summary:**

The area of a rectangle whose width is 6 feet, and the diagonal is 10 feet is 48 sq feet.