Question

find the value of x.
$x = \square$

Explanation:

Step1: Identify midsegment theorem

The figure shows that the segments of length 25 and 30 are midsegments of the larger triangle, meaning they connect midpoints of the triangle's sides. By the triangle midsegment theorem, a midsegment is half the length of the side it is parallel to.

Step2: Sum twice the midsegments

The side $x$ is equal to twice the sum of the two midsegments.
$x = 2\times(25 + 30)$

Step3: Calculate the total value

First compute the sum inside the parentheses, then multiply by 2.
$x = 2\times55 = 110$

Answer:

$x = 110$