Question

△STU is an equalateral triangle, if ST is one less than twice x, SU Is 37 less than 5 times x, and TU is 11 more than x, find x and the measurement of each side ​

Answer 1

Answer:

x = 12, sides = 23

Step-by-step explanation:

$\overline{ST}=2x-1\\\overline{SU}=5x-37\\\overline{TU}=x+11$

Since $\triangle{STU}$ is equilateral, all three sides are equal. Therefore:

$\left[\begin{array}{l}y=2x-1\\y=5x-37\\y=x+11\end{array}\right]$

Substituting y = x + 11:

$\left[\begin{array}{l}x+11=2x-1\\x+11=5x-37\end{array}\right]$

Solving for x:

$x+11=2x-1\\11=x-1\\12=x$

Substituting x = 12:

$y=x+11\\y=12+11\\y=23$

Thus, x = 12 and the length of each side is 23.