Question

A 55-inch television screen has a shape of a rectangle with a diagonal that is 55 inches long and a width of the screen is 27 inches.

What is the perimeter of the screen?



Enter your answer, rounded to the nearest hundredth, in the box.


in.

Answer 1

Perimeter of the rectangle = 149.84 inches.

Explanation:

Given : A 55-inch television screen has a shape of a rectangle with a diagonal that is 55 inches long and a width of the screen is 27 inches.

To find : What is the perimeter of the screen?

Solution :

Diagonal of the rectangular screen is D=55 inches

The width of the screen is W= 27 inches

Rectangle all angles are of 90°

Apply Pythagorean theorem,

`D^2=L^2+W^2`

`55^2=L^2+27^2`

`L^2 = 55^2 - 27^2`

`L^2 = 3025 -729`

`L^2 = 2296`

`L = √(2296)`

`L= 47.92 in.`

Length L=47.92

Perimeter of the rectangle = 2(L+W)

Perimeter of the rectangle = 2(47.92+27)

Perimeter of the rectangle = 2(74.92)

Perimeter of the rectangle = 149.84 inches.

Answer 2

L^2 = 55^2 - 27^2

L^2 = 3025 - 729
L^2 = 2296
L = sqrt(2296) = 47.92 inches

perimeter = 27*2 + 47.92*2 = 54 + 95.84 = 149.84 inches