SOLUTION: The width of a rectangular TV screen is 14.5 cm more than the height. If the diagonal is 68.6 cm, find the dimensions of the screen.

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Question 1022144: The width of a rectangular TV screen is 14.5 cm more than the height. If the diagonal is 68.6 cm, find the dimensions of the screen.
Answer by ikleyn(52810) About Me  (Show Source):
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The width of a rectangular TV screen is 14.5 cm more than the height.
If the diagonal is 68.6 cm, find the dimensions of the screen.
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Let x be the height measure in centimeters.
Then the width measure is (x + 14.5), in accordance with the condition.
The diagonal is (Pythagorean theorem)

sqrt%28x%5E2+%2B+%28x%2B14.5%29%5E2%29.

According with the condition, the diagonal measure is 68.6 cm.

It gives you an equation

x%5E2+%2B+%28x%2B14.5%29%5E2 = 68.6%5E2.

Simplify it:

x%5E2+%2B+x%5E2+%2B+29x+%2B+14.5%5E2+-+68.6%5E2 = 0,

2x%5E2+%2B+29x+-+4495.71 = 0.

Apply the quadratic formula. You will get

x%5B1%2C2%5D = %28-29+%2B-+sqrt%2829%5E2+%2B+4%2A2%2A4495.71%29%29%2F4 = %28-29+%2B-+sqrt%2836806.68%29%29%2F4 = %28-29+%2B-+191.85%29%2F4.

The positive root (which only suits the condition) is 40.71.

The height of the screen is 40.71 cm.
The width is  40.71 + 14.5 = 55.21 cm.