length of shortest side of a right triangle

Question

The hypotenuse of a right triangle has a length of 20 inches. If one leg of the triangle is 3 times the other leg, what is the length of the shortest side of the triangle?

Answer 1

Hi Mich, use the Pythagorean Theorem to solve this problem. Let x represent one leg of the triangle, then the other leg is 3x in length.

 

C² = A² + B², where C = 20

 

20² = x² + (3x)²

 

Solve for x gives:

 

400 = x² + 9x²

 

400 = 10x²

 

Divide both sides by 10 gives:

 

x² = 40

 

x = √40

 

x ≈ 6.32 inches, or the shorter leg.

 

The longer leg is 3x, or about 18.97 inches.

 

Questions?

Answer 2

Hypotenuse (c) length is 20 inches

Let small side (a) have the length x inches

The bigger side (b) would have the length of 3x inches

We know that a² + b² = c²

 

That means: x² + 9x² = 20²

10 x² = 400

or: x = (40)^1/2

x= 6.3 inches