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
d2 = l2 + w2
(10)2 = l2 + (6)2
l2 = 100 - 36
l2 = 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.