Question

SP=2x+3, and LN=5x−14. Find SP. A. 20 B. 86 C. 43 D. 50

Answer 1

C

Explanation:

A segment joining the midpoints of two sides of a triangle is half the length of the third side.

SP is a midline segment, thus

SP =
`(1)/(2)` LN , that is

2x + 3 =
`(1)/(2)` (5x - 14) ← multiply both sides by 2

4x + 6 = 5x - 14 ( subtract 4x from both sides )

6 = x - 14 ( add 14 to both sides )

20 = x

Thus

SP = 2x + 3 = 2(20) + 3 = 40 + 3 = 43 → C