Question

The diagonal of a rectangle measures 65 centimeters. The length of the rectangle is 33 cen-

timeters. Consider the measurements to be exact.
Find the width of the rectangle.
Find the area of the rectangle.

Answer 1

`\large \boxed{\text{56 cm; 1848 cm}^(2)}`

Explanation:

The diagonal divides the rectangle into two right triangles.

A. Calculate the width of the rectangle

We can use Pythagoras' Theorem.

`\begin{array}{rcl}a^(2) + b^(2) & = & c^(2)\\a^(2) + 33^(2) & = & 65^(2)\\a^(2) +1089 & = & 4225\\a^(2) & = & 3136\\a & = & \mathbf{56}\\\end{array}\\\text{The width of the triangle is $\large \boxed{\textbf{56 cm}}$}`

B. Calculate the area of the rectangle

The formula for the area A of a rectangle is

A = lw = 33 cm × 56 cm = 1848 cm²