Question

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The following is an isosceles trapezoid, find RS

Answer 1

The length of RS is 47 units

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=(RS+UT)/(2)`

Substituting the variable lengths of the sides:

`\displaystyle 3x+5=(2x+15+6x-37)/(2)`

Operating:

`\displaystyle 3x+5=(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