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eimsori
2 months ago
5

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

Mathematics
1 answer:
tester [12.3K]2 months ago
6 0

Answer:

QS=68\ units

Detailed solution process:

Step 1:

Determine the value of x.

Given that R is the midpoint of QS, it follows that

QR equals RS.

Therefore,

QS equals QR plus RS, which is QS equals 2 times RS — this is equation A.

Also,

RT equals RS plus ST — this is equation B.

Refer to the accompanying diagram for clarity.

Substitute known values into 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:

Calculate RS.

RS=2x-4

Replace x with its found value.

RS=2(19)-4

RS=34\ units

Step 3:

Calculate QS.

Recall equation A:

QS equals twice RS, so

QS=2(34)=68\ units

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