Question

Equilateral triangle mnp has perimeter 12a+18b. line segment qr is a midsegment. what is qr?

Answer 1

Let the triangle be abc  with equal sides ab,bc and ca
then perimeter = 3 ab  = 12a + 18b

ab = = 4a + 6b  ( each side  will have this length)

Now since qr is a mid segment  it will be = half length of ab 

So qr = 2a + 3b  Answer

Answer 2

Answer:

qr = 2a + 3b

Step-by-step explanation:

First, we must calculate the measure of each side based on the perimeter. Since all three sides of an equilateral triangle are equal, we divide the perimeter by 3.

$\frac{12a+18b}{3}$

$\frac{12a}{3}+\frac{18b}{3}$

4a + 6b (measure of each side)

Being an equilateral triangle, any middle segment is half the length of any of its sides.

So, the value of qr is:

$qr = \frac{4a+6b}{2}\\qr = \frac{4a}{2} + \frac{6b}{2} \\qr = 2a + 3b$

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Hope this hepls!