SOLUTION: The longer leg of a right triangle is 3 inches longer than x, the length of the shorter leg. The hypotenuse is 15 inches long. The following equation shows the relationship between

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Question 886: The longer leg of a right triangle is 3 inches longer than x, the length of the shorter leg. The hypotenuse is 15 inches long. The following equation shows the relationship between the sides of the triangle.

x^2+(x+3)^2=225
What is the length of the shorter leg?
Answer by usyim88hk(157) About Me  (Show Source):
You can put this solution on YOUR website!
first of all, let's solve for (x+3)^2
(x+3)(x+3)
x(x+3)+3(x+3)
x^2+3x+3x+9
x^2+6x+9
Then put this into the equation
x^2+x^2+6x+9=225
2x^2+6x+9=225
Now subtract both sides by 225 to make both sides equal to zero
2x^2+6x-216=0
Use the quadratic formula
+x=%28%28-6%2B-sqrt%28%28-6%29%5E2-4%282%29%28-216%29%29%29%2F%282%282%29%29%29+
+x=%28%28-6%2B-sqrt%2836%2B1728%29%29%2F4%29+
+x=%28%28-6%2B-42%29%2F4%29+
x=(-48/4) or (36/4)
x=-12 or 9
Since length cannot be negative number, -12 is not the answer, so 9 is the length of the shorter leg.
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check: 9^2+(9+3)^2=225
81+144=225
225=225 (correct!!!)