Question

You have just bought a new television and it has an aspect ratio of 16:9. The screen on the television is 65 inches. What is the width, height, and area of the telev a. width 56.65 inches, height 31.86 inches, area 1804.55 square inches b. width 16 inches, height 9 inches, area 144 square inches o c. width 42.59 inches, height 21.22 inches, area 903.76 square inches d. width 31.87 inches, height 45.02 inches, area 1,434.78 square inches

Answer 1

A

Explanation:

The TV to have a 16:9 ratio and have a diagonal of 65 inches must have a length & width whose squares add to 4,225 (65 squared) and whose ratio length and width simplifies to 16/9.

B is not an option because
`16^2+9^2\\eq 65^2`.

C is not an option because
`(42.59)/(21.22)\\eq (16)/(9)` which is 1.777777777778 as a decimal.

D fails for the same reason as C.

Therefore A is the solution because
`(56.65)/(31.86)=(16)/(9)` and
`65.65^2+31.86^2 = 65^2`