Question

The length of the longer leg of a right triangle is 13 m more than three times the length of the shorter leg. The length of the hypotenuse is 14 m more than three times the length of the shorter leg. Find the side lengths of the triangle.

Answer 1

Step 1 :

Set up the right triangle with the following:

side a = x

side b = 13 + 3x

side c = 14 + 3x

Using pythagorean theorem :

`a^2+b^2=c^2`

`x^2+(13+3x)^2=(14+3x)^2`

Step 2 :

Expand this equation by using foil to get:

`x^2+(169+78x+9x^2)=196+84x+9x^2`

Simplifying this equation will give you:

`x^2\text{ - 6 x - 27 = 0}`

Step 3 :

Factor this to get:

(x-9)(x +3) = 0

Solving this will give you x = 9 or x = -3.

The side length cannot be negative so discard the -3.

Step 4 :

Your side lengths will be:

`\begin{gathered} a\text{ = x = 9 m} \\ b\text{ = 13 + 3 x = 13 + 3 ( 9 ) = 13 + 27 = 40 m} \\ \text{c = 14 + 3 x = 14 + 3 ( 9 ) = 14 + 27 = 41 m} \end{gathered}`

CONCLUSION:

The side lengths of the triangle are:

9 m , 40 m and 41 m