Question

What is the value of m in the figure below? If necessary, round your answer to

the nearest tenth of a unit.
A. 18
B. 13.2
C. 12.5
D. 7

Answer 1

First

`\\ \sf\longmapsto BD^2=AD* DC`

`\\ \sf\longmapsto BD^2=18^2+7^2`

`\\ \sf\longmapsto BD^2=324+49`

`\\ \sf\longmapsto BD^2=363`

`\\ \sf\longmapsto BD=√(363)`

`\\ \sf\longmapsto BD=19.2`

Now

Using Pythagorean theorem

`\\ \sf\longmapsto BD^2+CD^2=m^2`

`\\ \sf\longmapsto m^2=7^2+19.2^2`

`\\ \sf\longmapsto m^2=49+363`

`\\ \sf\longmapsto m^2=412`

`\\ \sf\longmapsto m=√(412)`

`\\ \sf\longmapsto m=20.3`

Nearest value in options is 18

Hence option a is correct