Question 135922
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?