LMN is a right-angle triangle. Angle NLM=90. PQ is parallel to LM. The area of triangle PNQ is 8cm^2. The area of triangle LPQ is 16cm^2. Work out the area of triangle

The area of LQM is

Step-by-step explanation:

Given

Area of PNQ = 8

Area of LPQ = 16

See attachment for triangles

The area of PNQ is calculated as:

Substitute 8 for Area

The area of LPQ is calculated as:

Substitute 16 for Area

From the attachment:

Make LP the subject

So:

We have:

and

Equate both expressions:

Divide both sides by PQ

Multiply both sides by 2

Since PNQ is similar to LNM, the following equivalent ratios exist:

Substitute

Area of LQM is:

This gives:

Recall that:

So: