Finding the side lengths of a triangle

Question

The shortest leg of a triangle is 17 feet shorter than the other leg. The hypotenuse of this triangle is 25 feet. What are the lengths of the two legs of this triangle?

 

I do do not know where to even begin this problem. Where do I start? 

Answer 1

Ingrid was really close to the answer.

 

We do in fact, have a right triangle. The sum of the squares of the legs is indeed the square of the hypotenuse.

 

One of your legs is 17 feet shorter than the other. If we call the longer leg X, then the shorter leg is X - 17

 

Add the squares of these two and equate them to 25 squared.

 

(X - 17)² + X² = 25²

 

Note that that first square requires us to FOIL it out.

 

X² - 34X + 289 + x² = 625

2X² - 34X - 336 = 0

 

Factoring this looks very challenging, so let's use the quadratic formula instead.

 

X = [-b +/- sqrt( b² -4ac) ] / 2a

 

We find that X = -7 or 24

 

Can lengths have a negative value? No, they cannot, so X = 24.

 

Checking this we get...

 

24² + (24 - 17)²

24² + 7² 

576 + 49

625

 

Now the right side... 25² = 625

 

So we have the correct value of X, which is 24.

 

The legs have lengths of 24 feet and 7 feet.

Answer 2

If a and b are the lengths of the legs of a right triangle and c is the length of the hypotenuse, then the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.

This relationship is represented by the formula:  A(squared)+B(Squared) =C (Squared)

 

 

To square a number means to multiply it by itself.the sum of the squares of the lengths of both legs is the same as the square of the length of the hypotenuse.

 

The two "legs" of a right triangle are the two sides of the triangle that have the same or very close to the same measurement. The Hypotenuse is the longest side of the triangle you are measuring.given the measurements for the hypotenuse, c, and one leg, b. The hypotenuse is always opposite the right angle and it is always the longest side of the triangle.

 

So if  the hypotenuse is 25 feet and one leg is 17 feet shorter than the other leg, you would find the square root of 25 which is 5 and then you would multiply on your calculator and find the square root of  25 (squared) and take the hypotenuse and subtract the known varible to get the number of one side and then square it,in this case if you take 25-17 you are left with 8 to square which will be 64. So you add  25 and 64 and get 89 =C (Squared) and use your calculator to find the closest square root to the 10ths place of 89 and that is your answer.