Question

Find the value of x ? So I tried it

Answer 1

You need to understand what the concept behind this problem is. Usually, in a triangle, adding measures and setting the sum equal to 180 is done when you know the measures of the 3 angles of a triangle since the sum of the measures of a triangle equals 180. Here, the expressions are the lengths of two sides of two different triangles.

Here is what you need to know to solve this problem.

First, here's a definition:

A midsegment of a triangle is a segment that has as endpoints the midpoints of two sides of the triangle.

Look at the big triangle above. The left side is separated into two congruent segments. The point in the middle is the midpoint of that side. The right side of the big triangle is also separated into two congruent segments. The point in the middle is the midpoint of that side. The segment labeled x + 5 is a midsegment of the large triangle since it joins the midpoints of two sides of the triangle.

Here is a theorem about the midesgment of a triangle.

The midsegment of a triangle is a segment that has as endpoints the midpoints of two sides of a triangle. The midsegment is parallel to and half the length of the third side of the triangle.

The part you need is "The midsegment is parallel to and half the length of the third side of the triangle." The midsegment that measures x + 5 is half the length of the segment that measures 3x - 1. Now we can write an equation and solve for x.

$x + 5 = \dfrac{1}{2}(3x - 1)$

Multiply both sides by 2.

$2(x + 5) = 3x - 1$

$2x + 10 = 3x - 1$

Subtract 3x from both sides. Subtract 10 from both sides.

$-x = -11$

Multiply both sides by -1.

$x = 11$

There you have x = 11 which as you know is the correct answer, and now you know why. Please ask any questions if it is not clear.