SOLUTION: please help me about this problem : one leg of a right triangle is 1 cm longer than the other leg, and the hypotenuse is 2 cm longer than the shorter leg. Find the lengths of the t

Question 501665: please help me about this problem : one leg of a right triangle is 1 cm longer than the other leg, and the hypotenuse is 2 cm longer than the shorter leg. Find the lengths of the three sides of the triangle.I think the legs are 3 and 4 cm and the hypotenuse is 5 cm. but iam not sure about it, i need a solution and some explanation for this, i will also report this tomorrow on our class. please help me. thank you.
Answer by geetha_rama(94) (Show Source): You can put this solution on YOUR website!
Yes you are correct.
Here's explanation:
Let X be the length of shorter leg
Y be the length of longer leg
Z be the length of hypotensue.
From the problem , we have
Y = X + 1 ( longer leg is 1cm more than shorter leg)
Z = X+ 2 (hypotenuse is 2cm longer than the shorter leg)
We know that
X^2 + Y^2 = Z^2
Substituting values for Y and Z,
X^2 + (X+1)^2 = (X+2)^2
X^2 + X^2 + 2*X + 1 = X^2 + 4*X + 4
X^2 -2*X -3 = 0
X^2 -3X + X - 3 = 0
X(X-3) + 1(X-3)= =
(X-3)(X+1) = 0
X = 3, -1
Length should be positive.
Hence Shorter leg X = 3cm, Longer leg Y = 4cm and Hypotenuse Z = 5 cm
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