Question

A, B, and C are midpoints of ∆GHJ. When AB = 3x+8 and GJ = 2x+24, what is AB?​

Answer 1

AB = 14 units

Explanation:

Given:

A triangle GHJ with the following aspects:

A, B, C are midpoints of sides GH, HJ and GJ respectively.

AB =
`3x+8`

GJ =
`2x+24`

Midsegment Theorem:

The line segment joining the midpoints of any two sides of a triangle is parallel to the third side and the length of the midsegment is one-half of the length of the third side.

Therefore, AB is the midsegment of sides GH and HJ and thus, is parallel to GJ and equal to one-half the length of GJ.

`\therefore AB=(1)/(2)*\ GJ`

Now, plug in the values of AB and Gj and solve for 'x'.

This gives,

`3x+8=(1)/(2)(2x+24)\\\\3x+8=x+12\\\\3x-x=12-8\\\\2x=4\\\\x=(4)/(2)=2`

Now, the length of AB is given by plugging in 2 for 'x'.

`AB=3*2+8=6+8=14`

Therefore, the length of midsegment AB is 14 units.