Question

Let MF = 3x - 4 and BM = 5x - 5

Answer 1

Step-by-step explanation:

a)Here, we want to get the value of x

Mathematically, we know that for a triangle with median M, the length of one of the sides is two times the length of the other side of the median

We have this as:

`BM\text{ }=\text{ 2MF}`

Using the side lengths given, we have it that:

`\begin{gathered} 5x-5\text{ = 2(3x-4)} \\ 5x-5\text{ = 6x-8} \\ 6x-5x=8-5 \\ x\text{ = 3} \end{gathered}`

b) We want to find the length of MF. We just have to substitute the value of x in the expression for MP

Mathematically, we have this as:

`MF\text{ = 3(3)-4 = 9-4 = 5}`

c) We want to find the length of BM

`5x-5\text{ = 5(3)-5 = 15-}5\text{ = 10}`

d) Here, we want to find the length of BF

`\begin{gathered} BF\text{ = BM + MF} \\ BF\text{ = 10 + 5 = 15} \end{gathered}`