Question

SM=3x−4, and RN=9x−20. Find the value of x

Answer 1

Answer:

Option (A).

Step-by-step explanation:

Given question is incomplete; find the complete question with the attachment.

In the triangle NRL,

Points P, S and M are the midpoints of the sides NR, RL and LN respectively.

Sides SM = (3x - 4), NR = (9x - 20)

By the theorem of midpoints in a triangle,

SM = $\frac{1}{2}\text{NR}$

(3x - 4) = $\frac{1}{2}(9x-20)$

6x - 8 = 9x - 20

9x - 6x = 20 - 8

3x = 12

x = 4

Therefore, Option (A) will be the answer.

Answer 2

The value of x is equal t 4

Data;

• midpoint = SM = 3x - 4
• Length of line = 9x - 20

Midpoint of a Line

The midpoint of a line is half the distance of the line.

Since the length of the line is RN and midpoint of the line is SM.

$SM = \frac{1}{2} RN$

Let's substitute the values into the equation

$SM = \frac{1}{2} NR\\3x - 4 = \frac{1}{2}(9x- 20)\\ 3x - 4 = \frac{1}{2} (9x - 20)\\2(3x - 4) = 9x - 20\\6x - 8 = 9x - 20\\9x-6x = 20 - 8 \\3x = 12\\\frac{3x}{3} = \frac{12}{3} \\x = 4$

The value of x is equal t 4

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