Question

Image attached: Triangle measurement Theorem

Answer 1

Answer:

17

Step-by-step explanation:

Using Triangle Midsegment theorem, it states that if :

Q is the midpoint of MN and R is the midpoint of NP

Then, QR is parallel to MP and QR = 1/2 of MP

Mathematically

QR = 1/2MP

From the above question, we are given the following values:

QR = 3x - 4

MP = 55 - 3x

Since

QR = 1/2MP

3x - 4 = 1/2(55 - 3x)

3x - 4 = 55/2 - 3x/2

Collect like terms

3x + 3x/ 2 = 55/2 + 4

9x/ 2 = 31.5

Cross Multiply

9x = 31.5 × 2

9x = 63

x = 63/9

x = 7

Since QR = 3x - 4

x = 7

QR = 3×7 - 4

= 21 - 4

= 17

Hence, QR = 17