SOLUTION: A triangular garden in the shape of a right triangle has an area of 60m²
If the longest side is 2 meters longer than the next shorter side which is x meters long, derive the pol
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Question 1178000: A triangular garden in the shape of a right triangle has an area of 60m²
If the longest side is 2 meters longer than the next shorter side which is x meters long, derive the polynomial equation x³+x²-3600=0 and then solve for x.
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52754) (Show Source): You can put this solution on YOUR website!
Answer by greenestamps(13195) (Show Source): You can put this solution on YOUR website!
The longest side of a right triangle is the hypotenuse. In this problem, it is 2 longer than the next longest side, which has length x.
So the right triangle has long leg x and hypotenuse x+2.
The Pythagorean Theorem then gives us sqrt(4x+4) = 2*sqrt(x+1) as the length of the other leg.
The area of a right triangle is one-half the product of the lengths of the two legs; the area is given as 60:
Solve using a graphing calculator to find x=15 as the only real root.
ANSWER: x=15
Note that gives us the familiar 8-15-17 right triangle....
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