Question

in the diagram below of triangle PQR,S is a midpoint of PQ and T is a midpoint of QR. If ST=95-10x, and PR=55-5x, what is the measure of ST

Answer 1

The figure shows that segment ST is a midsegment of triangle PQR.

For this type of scenario, let's recall that the midsegment is equal to half of the length of the base of the triangle:

`\text{Midsegment = }(1)/(2)(Base\text{ Length)}`
`\text{ ST = }(1)/(2)PR`
`\text{ 95 - 10x = }(1)/(2)(55\text{ - 5x)}`
`(95\text{ - 10x)(2) = }(1)/(2)(55\text{ - 5x)(2)}`
`190\text{ - 20x = 55 - 5x}`
`190\text{ - 55 = -5x + 20x}`
`135\text{ = }15x\text{ }\rightarrow\text{ }(135)/(15)\text{ = }(15x)/(15)`
`\text{ x = 9}`

Since we've determined that x = 9. let's solve for the measure of ST by plugging in x = 9 in the equation.

`\text{ ST = 95 - 10x = 95 - 10(9)}`
`\text{ ST = 95 - 9}0`
`\text{ ST = 5}`

Therefore, ST = 5.