Question

435A triangle has sides 95 yards, 25 yards, and 32 yards. What is the perimeter (distance around the edges) of the8triangle in yards? Express your answer in mixed number form, and reduce if possible.

Answer 1

We are given the following three sides of a triangle.

`9(4)/(7),\; 2(3)/(4),\; 32(5)/(8)`

We are asked to find the perimeter of the triangle.

Recall that the perimeter of a triangle is the sum of all three sides.

`\begin{gathered} P=a+b+c \\ P=9(4)/(7)+\; 2(3)/(4)+\; 32(5)/(8) \end{gathered}`

Add the whole parts and the fractions separately,

`\begin{gathered} P=(9+2+32)((4)/(7)+\; (3)/(4)+\; (5)/(8)) \\ P=(43)((4)/(7)+\; (3)/(4)+\; (5)/(8)) \end{gathered}`

The LCM of 7, 4, 8 is 56

`\begin{gathered} P=43((4)/(7)+\; (3)/(4)+\; (5)/(8)) \\ P=43((8\cdot4+14\cdot3+7\cdot5)/(56)) \\ P=43((32+42+35)/(56)) \\ P=43(109)/(56) \end{gathered}`

Therefore, the perimeter of the triangle in the mixed form is 43 109/56 yards