SOLUTION: the hypotenuse of a right triangle is 12 inches and the area is 24 square inches. Find the dimension of the triangle, correct to one decimal place.

Question 1041173: the hypotenuse of a right triangle is 12 inches and the area is 24 square inches. Find the dimension of the triangle, correct to one decimal place.
Found 3 solutions by josgarithmetic, ikleyn, MathTherapy:
Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
x y h dimensions; h for hypotenuse

-

Solve first for ....

Graphing y=x^4-144x^2+24 through google.com shows that there are three real and apparently rational roots, so that degree-four polynomial is factorable.
Answer by ikleyn(52787)   (Show Source): You can put this solution on YOUR website!
.
The hypotenuse of a right triangle is 12 inches and the area is 24 square inches.
Find the dimension of the triangle, correct to one decimal place.
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= , (1) = , (2) or = , (1') = . (2') Multiply eqn. (2') by 2 and add to eqn(1') (both sides). You will get = , or = , or = = . Thus from (1) and (2) we got x + y = , (3) xy = 48. (4) Notice that in this way we decreased the degree of the original equations/system. It makes it easier to work in future with (3),(4) instead of (1),(2). Next, from (3) x = . Substitute it into (4) and get = . (5) = , Solve this quadratic equation by applying the quadratic formula. You will get = = = . Then = - . Answer. There are two solutions: a) x = , y = , and b) x = , y = . Check. a) = = 144, xy = 4*15 - 4*3 = 60 - 12 = 48. OK ! ! !

Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
the hypotenuse of a right triangle is 12 inches and the area is 24 square inches. Find the dimension of the triangle, correct to one decimal place.

Height and base:
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