SOLUTION: one leg of a right triangle is 12 cm longer than the other, and the area of the right triangle is 110 cm squared. Find the length of the longer leg

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Question 378147: one leg of a right triangle is 12 cm longer than the other, and the area of the right triangle is 110 cm squared. Find the length of the longer leg
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!


Hi

one leg of a right triangle is 12 cm longer than the other

Let x and (x+12cm) represent the lengths of the legs of this right triangle

A = (1/2)b*h

110cm^2 = (1/2)x(x+12cm)

220 = x^2 + 12x

0 = x^2 + 12 - 220

factoring

(x+22)(x-10)= 0 Note:SUM of the inner product(22x) and the outer product(-10x) = 12x

(x+22) = 0

x = -22 extraneous solution

(x-10)= 0

x = 10   10cm and 22cm are the lengths of the two legs

Letting c represent the length of the longer lefg & applying the Pythagorean Theorem

10^2 + 22^2 = c^2

584 = c^2  (discarding negative solution for length)

24.17cm  = c