Question

Find the value of x.

Answer 1

We have the similar triangles. Therefore the lengths of the sides are in proportion:

`(x)/(22)=(42)/(11+22)\\\\(x)/(22)=(42)/(33)\qquad\text{cross multiply}\\\\33x=(22)(42)\qquad\text{divide both sides by 33}\\\\x=((22\!\!\!\!\!\diagup^2)(42))/(33\!\!\!\!\!\diagup_3)\\\\x=((2)(42\!\!\!\!\!\diagup^(14)))/(\\ot3_1)\\\\x=(2)(14)\\\\\boxed{x=28}`