Question

Answer this easy geometry question. And no links, please.

Answer 1

x = 10

Explanation:

Since KL is parallel to HI

m∠JKL = m∠JHI

m∠JLK = m∠LIH

For the two triangles JKL and JHI, we have the common angle J and two angles equal to the corresponding two angles

Therefore the triangles are similar

Ratio of the sides to the corresponding sides must be equal

Hence

`(JH)/(JK) = (JI)/(JL)\\`

JH = JK + KH = 28 + 20 = 48

JI = JL + JL = 14 + x

Therefore

`(JH)/(JK) = (JI)/(JL)\\\\= > (48)/(28) = (14 + x)/(14)`

`(48)/(28) = (12)/(7)` by dividing numerator and denominator by 4

Hence

`(48)/(28) = (14 + x)/(14)\\\\\rightarrow \quad (12)/(7) = (14 + x)/(14)\\\\`

Multiply both sides by 14:

`14 \cdot (12)/(7) = 14 \cdot (14 + x)/(14)\\\\2 \cdot 12 = 14 + x\\\\24 = 14 + x\\\\\text{Subtract 14 both sides:}\\\\24 - 14 = x\\\\or\\\\x = 10\\\\`