Question

Can you solve for x?

Answer 1

x = 7

Explanation:

we can first note that the angles of both trapeziums are the same, and thus they are similar. so, one trapezium is a scaled version of the other.

let the two trapeziums be P and Q.

P has side 8 and Q has side 10, so there is a scale factor of 10/8, or 5/4.

next we have side 2x-2 in P, and 15 in Q.

so, we have the equation

`(5)/(4) = (15)/(2x - 2)`

next, we cross multiply and get

`5(2x - 2) = 15 * 4`

divide both sides by 5.

`2x - 2 = 3 * 4 = 12`

then, we can solve for x.

`2x - 2 = 12 \\ 2x = 14 \\ x = 7`