SOLUTION: the hypotenuse of a right triangle is 45 ft. if each leg were 6 feet shorter, the area would decreased by 17 sq.ft. Find the lenght of the legs
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Question 698352: the hypotenuse of a right triangle is 45 ft. if each leg were 6 feet shorter, the area would decreased by 17 sq.ft. Find the lenght of the legs Answer by KMST(5328) (Show Source):
You can put this solution on YOUR website! You most likely have a typo.
The triangle area should decrease by a lot more than 17 sq ft.
Otherwise there is no solution.
A decrease of 171 sq ft would work nicely.
It would give you legs 27 ft and 36 ft long.
I'll solve the problem for an area decrease of 171 sq ft.
= length of one leg (in feet) = length of the other leg (in feet)
The Pythagorean theorem says that -->
The area of a triangle is calculated as
Since the legs are perpendicular to each other,
we can calculate the area of the triangle,
taking one leg as the base and the other as the height.
Making each leg 6 feet shorter, the shortened leg lengths (in feet) would be and and the new triangle area (in square feet) would be
IF that equals square feet less than the area of the original triangle,
which we know is square feet, -->
Dividing both sides by 3, we simplify that to --> -->
Substituting that into the other highlighted equation, we get --> --> -->
Dividing everything by 2, we get the simpler equation
The solutions are (which makes ) and (which makes .
In any case, the lengths of the legs of the original triangle are feet and feet.
