Question

In a trapezoid TSRQ, TS H OR, U is the midpoint of TQ, and V is the midpoint of SR. If T5 = 8x+34,

UV
786, QR = 14x+92, find the value of x.
(Please help)

Answer 1

Explanation :

To find the value of x, we need to use the information given about the trapezoid and its midpoints.

First, we know that U is the midpoint of TQ. This means that the segment TU is equal in length to the segment UQ.

Similarly, V is the midpoint of SR. This means that the segment SV is equal in length to the segment VR.

Given that TS = 5, and UV = 786, we can set up the following equations:

TU + UQ = TS

UV + VQ = SR

Replacing the known values into the equations:

TU + UQ = 5

786 + VQ = SR

Since U is the midpoint of TQ, TU = UQ. Similarly, since V is the midpoint of SR, SV = VR. Therefore, we can simplify the equations as follows:

TU + TU = 5

786 + SV = SR

2TU = 5

786 + SV = SR

Since we are given the lengths of TS and QR in terms of x, let's substitute those values in:

2(8x + 34) = 5 (Equation 1)

786 + (14x + 92) = SR (Equation 2)

Now we can solve these equations to find the value of x.

Simplifying Equation 1:

16x + 68 = 5

16x = 5 - 68

16x = -63

x = -63/16

Therefore, the value of x is -63/16.