Question

Please Help! The following is an isosceles trapezoid, find RS

Answer 1

Answer:

The length of RS is 47 units

Step-by-step explanation:

Midsegment Theorem

The midsegment of a trapezoid is a line segment that connects the midpoints of the non-parallel sides.

The length of the midsegment of a trapezoid is the average of the lengths of the bases.

The midsegment of the given trapezoid is VW, and the bases are RS and UT.

According to the midsegment theorem:

$\displaystyle VW=\frac{RS+UT}{2}$

Substituting the variable lengths of the sides:

$\displaystyle 3x+5=\frac{2x+15+6x-37}{2}$

Operating:

$\displaystyle 3x+5=\frac{8x-22}{2}$

Dividing the fraction:

$3x+5=4x-11$

Rearranging:

$4x-3x=5+11$

Operating:

x=16

The length of RS is:

$RS=2x+15=2*16+15=32+15=47$

The lenght of RS is 47 units