Question

Jerry is buying a new large screen television for his game room. He knows that the diagonal of the television measures 42.1 inches and the base is 34.3 inches. What is the area of the television? (round to nearest tenth) A) 595.4 in2 B) 836.9 in2 C) 1027.2 in2 D) 1176.5 in2

Answer 1

836.9 in2

Explanation:

c2 = b2 + a2

42.12 = 34.32 + a2

a = 24.4115

then,

A = 34.3 x 24.4 = 836.92

Answer 2

Remember that the area of a rectangle is length times width; since we don't know the width, we'll use the Pythagorean theorem to find it first:

`l= \sqrt{h^(2)-c^(2) }`
Where l is the leg, and h the hypotenuse. We know that one of the legs, the base has a measures 34.3 inches and the hypotenuse a measures 42.1 inches.
Replace the values to get:

`l= \sqrt{42.1^(2)-34.3^(2) }`

`l=24.4=w`
Now that we know the width (w), we just net to multiply it by the length to get our area:

`A=(24.4)(34.3)=836.9`

We can conclude that the correct answer is B) 836.9 in.