Question

fill in the blank 1 point
given uv, vw, and uw and are midsegments, if ts = 42, uw = 23, and vw = 19, what is the perimeter of △rst?
perimeter = type your answer...

Explanation:

Step1: Use the mid - segment theorem

The mid - segment theorem states that the length of a mid - segment of a triangle is half the length of the side parallel to it.
If \(UW\) is a mid - segment, then \(RS = 2UW\). Given \(UW = 23\), so \(RS=2\times23 = 46\).
If \(VW\) is a mid - segment, then \(RT=2VW\). Given \(VW = 19\), so \(RT = 2\times19=38\).
We are given \(TS = 42\).

Step2: Calculate the perimeter of \(\triangle RST\)

The perimeter \(P\) of \(\triangle RST\) is \(P=RS + RT+TS\).
Substitute \(RS = 46\), \(RT = 38\), and \(TS = 42\) into the formula: \(P=46 + 38+42\).
First, \(46+38=(40 + 6)+(30 + 8)=70+14 = 84\).
Then, \(84 + 42=(80+4)+(40 + 2)=120+6=126\).

Answer:

126