Question

If r is the midpoint of qs rs=2x-4, st= 4x-1 and rt = 8x-43 find qs

Answer 1

`QS=68\ units`

Explanation:

step 1

Find the value of x

we know that

r is the midpoint of qs

so

QR=RS

QS=QR+RS------> QS=2RS -----> equation A

RT=RS+ST ----> equation B

see the attached figure to better understand the problem

Substitute the given values in the equation B and solve for x

`8x-43=(2x-4)+(4x-1)`

`8x-43=6x-5`

`8x-6x=43-5`

`2x=38`

`x=19`

step 2

Find the value of RS

`RS=2x-4`

substitute the value of x

`RS=2(19)-4`

`RS=34\ units`

step 3

Find the value of QS

Remember equation A

QS=2RS

so

`QS=2(34)=68\ units`