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One leg of a right triangle is 7 inches longer than the other leg, and the hypotenuse is 35 inches. Find the lengths of the legs of the triangle.

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1 vote

Answer: 21, 28

Explanation:

  • Side #1 = x
  • Side #2 = x + 7
  • Hypotenuse = 35

Use the Pythagorean Theorem
a^(2)+b^(2)=c^(2):

  • a = x
  • b = x + 7
  • c = 35

Substitute in the values & solve:


x^(2)+(x+7)^(2)=35^(2)\\x^(2)+x^(2)+14x+49=1225\\2x^(2)+14x+49-1225=0\\2x^(2)+14x-1176=0\\2(x^(2)+7x-588)=0\\2(x + 28)(x - 21)=0\\x_(1)=-28, x_(2)=21

-28 is not a possible solution since you can't have negative inches...

  • a = x = 21
  • b = x + 7 = 21 + 7 = 28
  • c = 35
User Logan Kitchen
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