Question

in the diagram of NRQ below, SP||RQ,NS=12,SR=78, and NP=2 what isntje length of NQ?

Answer 1

Explanation:

We are told SP is parallel to RQ. So we would apply similar triangles theorem

Ratio of the corresponding sides of the triangles are equal

Ratio of the corresponding sides of small to big triangle

NS/NR = NP/NQ

NS=12, SR=78, and NP=2

NR = NS + SR

NR = 12 + 78

NR = 90

12/90 = 2/NQ

$\begin{gathered} \frac{2}{15}=\frac{2}{NQ} \\ \text{cross multiply:} \\ 2(NQ)\text{ = 2(15)} \\ NQ\text{ = 30/2} \\ NQ\text{ = 15} \end{gathered}$