Question

If MN, NO and MO are midsegments, find the perimeter of triangle JKL.

Answer 1

The perimeter of JKL is 138

Here, we want to find the perimeter of triangle JKL

Mathematically, this is the sum of the sides of the triangle

We have two sides but we are left with MO

We can get this by getting the value of x

Mathematically, by the mid-segment theorem, the side of the bigger triangle is two times the sides of the smaller triangle that is parallel to it

We have this as;

`\begin{gathered} 2(6x-1)\text{ = 13x-10} \\ 12x-2\text{ = 13x-10} \\ 13x-12x=-2+10 \\ x\text{ = 8} \\ \\ \text{Thus;} \\ MO\text{ = 6x-1 = 6(8)-1 = 48-1 = 47} \end{gathered}`

Mathematically, we have the perimeter as;

`\text{JKL = 47 + 42 + 49 = 138}`