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16.07.2022 - 01:21

The diagonal of TV is 26 inches long. One side is 14 inches longer than the other side. Find the length and width of the TV screen.

Question:

The diagonal of TV is {eq}\displaystyle 26 {/eq} inches long. One side is {eq}\displaystyle 14 {/eq} inches longer than the other side. Find the length and width of the TV screen.

Answers (1)

Venita April 4, 2023 в 14:48

Let the length of the shorter side be x. Then the length of the other side, which is 14 inches longer, is x + 14. We can use the Pythagorean theorem to relate the diagonal and the sides of the TV: (diagonal)^2 = (length)^2 + (width)^2 Substituting the given values: 26^2 = x^2 + (x+14)^2 Simplifying: 676 = 2x^2 + 28x + 196 2x^2 + 28x - 480 = 0 x^2 + 14x - 240 = 0 Factoring: (x + 20)(x - 12) = 0 x = -20 or x = 12 Since the length of a side cannot be negative, we take x = 12. Then the length of the other side, x + 14, is 26. Therefore, the length of the TV screen is 26 inches and the width is 12 inches.

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