Question

Someone please help I CAN'T SOLVE THIS I NEED TO FIND M AND Z ​

Answer 1

m =
`(16)/(3)` , z =
`(24)/(5)`

Explanation:

Δ PQT and Δ PRS are similar ( by AA postulate ), so the ratios of corresponding sides are equal, that is

`(PQ)/(PR)` =
`(PT)/(PS)` , substitute values

`(m-2)/(m)` =
`(5)/(8)` ( cross- multiply )

8(m - 2) = 5m ← distribute parenthesis on left side

8m - 16 = 5m ( subtract 5m from both sides )

3m - 16 = 0 ( add 16 to both sides )

3m = 16 ( divide both sides by 3 )

m =
`(16)/(3)`

and

`(QT)/(RS)` =
`(PT)/(PS)` , substitute values

`(3)/(z)` =
`(5)/(8)` ( cross- multiply )

5z = 24 ( divide both sides by 5 )

z =
`(24)/(5)`