Question

What is the value of a?

Answer 1

`\huge\boxed{a=(16)/(3)=5(1)/(3)}`

Explanation:

`\triangle ZYW\sim\triangle WYX\ (AAA)\\\\\text{Therefore corresponding sides are in proportion}\\\\(YX)/(YW)=(YW)/(ZY)\\\\\text{substitute}\\\\YX=a;\ YW=4;\ ZY=3\\\\(a)/(4)=(4)/(3)\qquad\text{multiply both sides by 4}\\\\4\cdot(a)/(4)=4\cdot(4)/(3)\qquad\text{cancel 4}\\\\a=(16)/(3)`