Question

The length of a rectangle is 16 centimeters, and the diagonal of the rectangle is 20 centimeters long. what is the perimeter of the rectangle

Answer 1

Find the width:

a² + b² = c²
16² + b² = 20²
b² = 20² - 16²
b² = 400 - 256
b² = 144
b = √144
b = 12

Find the perimeter:

Perimeter = 2 (Length + Width)
Perimeter = 2 (16 + 12)
Perimeter = 2 (28)
Perimeter = 56

Answer: 56 cm

Answer 2

The perimeter is 56 units.
The width of the rectangle (and subsequently, the perimeter) can be found using the Pythagorean theorem. The diagonal of the rectangle acts as the hypotenuse of a right triangle with the length being one of the legs.

Set up the equation like so:
`16^2+b^2=20^2` (remembering that Pythagorean theorem is
`a^2+b^2=c^2`).

Simplify to
`256+b^2=400`.

Subtract 256:
`b^2=144`

Calculate that
`b=12` from squaring both sides. Therefore, the width equals 12.

The perimeter of a rectangle is
`P=2L+2W`, where L, the length, is 16, and W, the width, is 12.

You find that the perimeter is 56 units.