SOLUTION: The hypotenuse of a right angled traingle is 34cm.Find the length of the other two sides if one is 14cm longer than the other.

Question 135922: The hypotenuse of a right angled traingle is 34cm.Find the length of the other two sides if one is 14cm longer than the other.
Answer by nycsharkman(136) (Show Source): You can put this solution on YOUR website!
The hypotenuse of a right angled triangle is 34cm. Find the length of the other two sides if one is 14cm longer than the other.
We use the Pythagorean Theorem:
a^2 + b^2 = c^2
Before we do, let's figure out the other parts of the question.
c^2 = our hypotenuse
The length of one side is 14 more than the other.
From this information, I pick up that one side = x and the other side = x + 14
We now have this:
Let a^2 = x
Let b^2 = (x + 14)
Let c^2 = 34
We now plug and chug.
x^2 + (x + 14)^2 = 34^2
x^2 + x^2 + 28x + 196 = 1156
2x^2 + 28x + 196 = 1156
2x^2 + 28x + 196 - 1156 = 0
2x^2 + 28x - 960 = 0
Divide every term by 2 to make factoring easier.
x^2 + 14x - 480 = 0
We now factor the left side.
(x + 30) (x - 16) = 0
Set each factor to 0 and solve for x.
x + 30 = 0
x = -30....This answer is REJECTED because length indicates distance and distance CANNOT be negative. It's like saying the distance from home plate to first base is -90 feet. Does that make sense? No! The distance is 90 feet NOT NEGATIVE 90 feet.
Back to your question.
x - 16 = 0
x = 16cm
One side of your triangle is 16cm.
The other side is x + 14cm.
To find it, replace x with 16cm and add to 14cm.
Other side of triangle = 16cm + 14cm = 30cm
Is this clear?

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