Question

given $overline{uv}$, $overline{vw}$, $overline{uw}$, are midsegments, if $ts = 42$, $uw = 23$, and $vw = 19$, what is the perimeter of $\triangle{rst}$? perimeter of $\triangle{rst}=$ select 84 126 105 72

Explanation:

Step1: Recall mid - segment theorem

The length of a mid - segment of a triangle is half the length of the side of the triangle it is parallel to.

Step2: Find the lengths of the sides of $\triangle{RST}$

Since $UW$ is a mid - segment parallel to $RS$, then $RS = 2\times UW$. Given $UW = 23$, so $RS=2\times23 = 46$.
Since $VW$ is a mid - segment parallel to $RT$, then $RT = 2\times VW$. Given $VW = 19$, so $RT = 2\times19=38$.
We are given $TS = 42$.

Step3: Calculate the perimeter of $\triangle{RST}$

The perimeter $P$ of $\triangle{RST}$ is $P=RS + RT+TS$. Substitute the values: $P = 46+38 + 42$.
$P=126$.

Answer:

126