The hypotenuse is 9feet longer than the side along the building. The third side is 7feet longer than the side along the building. Find the lengths of all three sides of the reflecting pool.
Answers
the leg along the wall is 8, the other leg is 8+ 7 or 15. The hypotenuse would be 8 + 9 or 17.
Step-by-step explanation:
Right triangles have the following relationship between their legs and hypotenuse where a and b are the lengths of the legs and c is the length of the hypotenuse:
a^2 + b^2 = c^2
For this problem, we can say that a is x and b is x + 7. The hypotenuse would be x + 9
Using these terms we can write this equation and solve for x:
x^2 + (x + 7)^2 = (x+9)^2
Expanding the terms gives:
x^2 + x^2 + 14x + 49 = x^2 +18x +81
Combine like terms:
2x^2 + 14x + 49 = x^2 + 18x + 81
Subtract x^2 from both sides of your equation:
2x^2 -x^2 + 14x + 49 = x^2 -x^2 +18x + 81
Then:
x^2 + 14x + 49 = 18x + 81
Subtract 18x from both sides :
x^2 + 14x -18x + 49 = 18x -18x +81
x^2 -4x +49 = 81
Subtract 81 from both sides:
x^2 -4x +49 -81 = 81-81
The result is: x^2 - 4x -32 = 0
This equation can be factored as (x-8) * (x + 4) = 0
The only positive solution is x= 8
Therefore the leg along the wall is 8, the other leg is 8+ 7 or 15. The hypotenuse would be 8 + 9 or 17.
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Hope it helps
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