Question

In a triangle XYZ, AB is a midsegment. Find the length of AB.

A. 25
B. 31
C. 30
D. 35

Answer 1

Option A.
`AB=25\ units`

Explanation:

step 1

Find the value of x

we know that

If AB is a mid-segment, then AB is parallel to YZ

so

Triangles AXB and YXZ are similar by AA Similarity Theorem

Remember that

If two figures are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent

In this problem

`(YZ)/(AB)=(YX)/(AX)`

we have that

`AB=(1)/(2)YZ` ----> by Midpoint Theorem

`YZ=2AB`

substitute the given values in the expression above

`(2AB)/(AB)=(22+2x+2)/(2x+2)`

solve for x

`2=(24+2x)/(2x+2)`

Multiply by (2x+2) both sides

`4x+4=2x+24`

Group terms

`4x-2x=24-4`

`2x=20`

`x=10`

step 2

Find the length of AB

`AB=3x-5`

substitute the value of x

`AB=3(10)-5=25\ units`