Question

If QR = 3x; LM - 8x -17; and ST = 31 calculate LM.

Answer 1

`\huge \boxed{23}`

Explanation:

QR < LM < ST

LM is the middle segment, it is in between the length of QR and ST.

LM is also the average or mean of QR and ST.

(QR+ST)/2 = LM

(3x+31)/2 = 8x-17

Multiply both sides by 2.

(2)(3x+31)/2 = (2)8x-17

3x + 31 = 16x - 34

Subtract 16x and 31 from both sides.

3x + 31 - 16x - 31 = 16x - 34 - 16x - 31

-13x = -65

Divide both sides by -13.

(-13x)/-13 = -65/-13

x = 5

Substitute x = 5 for LM.

8(5) - 17

40 - 17

= 23

Answer 2

5

Explanation:

The midsegment of a trapezoid is equal to one half the sum of the bases.

1. Set up the equation using the midsegment formula: 1/2 (QR + ST)

1/2 (3x + 31) = 8x - 17

2. Solve

1.5x + 15.5 = 8x - 17

32.5 = 6.5x

x = 5