The longest side of a right triangle is 1 ft longer than three times the length of the shortest side.

Question

Need length of the shortest side, the other side, and the longest side. 

 

The longest side of a right triangle is 1 ft longer than three times the length of the shortest side. The other side of the triangle is 1 ft shorter than three times the length of the shortest side. Find the lengths of the sides of the triangle.

Answer 1

The longest side of a right triangle is the hypotenuse, which we can call c. The other two sides can be called a and b. We can let b be the shortest side.

 

So, c = 3b + 1

and

a = 3b - 1

 

We can use the Pythagorean theorem to relate a, b and c.

 

c^2 = a^2 + b^2

 

Substituting, we get

 

(3b + 1)^2 = (3b - 1)^2 + b^2

 

9b^2 6b + 1 = 9b^2 -6b + 1 + b^2

 

The 9b^2 and 1's cancel.

 

6b = -6b + b^2

 

b^2 = 12b

 

Cancel out a b.

 

b = 12

So, a = 3b - 1 = 3(12) - 1 = 36 - 1 = 35

and

c = 3b + 1 = 3(12) + 1 = 36 + 1 = 37

 

So, the triangle is a 12-35-37 triangle