Question

A rectangular television screen is sold by the length of its diagonal. If the diagonal is 45 inches and the height of the screen is 27 inches, what is the area of the screen?​

Answer 1

Answer: 972 square inches

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Step-by-step explanation:

Draw a rectangle and one diagonal. Two identical triangles form. Focus on one of those triangles.

We have a right triangle with leg a = 27 and leg b = unknown. These represent the dimensions of the rectangular TV screen.

The hypotenuse is the diagonal which is c = 45.

Let's use the pythagorean theorem to find b.

`a^2 + b^2 = c^2\\\\27^2 + b^2 = 45^2\\\\729 + b^2 = 2025\\\\b^2 = 2025 - 729\\\\b^2 = 1296\\\\b = √(1296)\\\\b = 36\\\\`

This screen is 27 inches by 36 inches.

area = length*width = 36*27 = 972 square inches