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Algebra

Perimetre of a rectangle given is 34mThe length of a diagnol given is 13mFind the dimensions?

Answer

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July 14, 2009 3:52AM

In the rectangle ABCD, let the length be x, so the width will be 17 - x (17 = 1/2 of the perimeter). In the right triangle ABC, we have:

1. The length measure of AB = x (leg)

2. The length measure of BC = 17 - x (leg)

3. The length measure of AC = 13 (hypotenuse) From the Pythagorean Theorem we have: 13^2 = x^2 + (17 - x)^2

13^2 = x^2 + 17^2 - 2(17)(x) + x^2

169 = 2x^2 + 289 - 34x

0 = 2x^2 - 34x + 120

0 = x^2 - 17x + 60

x = [[-(-17) ± √[17^2 - 4(1)(60)]]/(2)(1)

x = [17 ± √(289 - 240)]/2

x = (17 ± √49)/2

x = (17 ± 7)/2

x = (17 + 7)/2 or x = (17 - 7)/2

x = 24/2 or x = 10/2

x = 12 or x = 5 17 - x = 17 - 12 or 17 - x = 17 - 5 17 - x = 5 or 17 - x = 12

Thus, the length measure is 12 m, and the width measure is 5 m, or

the length measure is 5 m, and the width measure is 12 m.