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Vaselesa [24]
3 years ago
9

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 i

s 16cm^2. Work out the area of triangle
Mathematics
1 answer:
likoan [24]3 years ago
5 0

Answer:

The area of LQM is 48cm^2

Step-by-step explanation:

Given

Area of PNQ = 8

Area of LPQ = 16

See attachment for triangles

The area of PNQ is calculated as:

Area = \frac{1}{2} * PQ * PN

Substitute 8 for Area

8 = \frac{1}{2} * PQ * PN

PQ * PN = 16

The area of LPQ is calculated as:

Area = \frac{1}{2} * PQ * LP

Substitute 16 for Area

16= \frac{1}{2} * PQ * LP

From the attachment:

PN + LP =LN

Make LP the subject

LP = LN -PN

So:

16= \frac{1}{2} * PQ * (LN -PN)

We have:

16= \frac{1}{2} * PQ * (LN -PN) and PQ * PN = 16

Equate both expressions:

\frac{1}{2} * PQ *(LN - PN) = PQ * PN

Divide both sides by PQ

\frac{1}{2} (LN - PN) = PN

Multiply both sides by 2

LN - PN = 2PN

LN= 3PN

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

\frac{LM}{PQ} = \frac{LN}{PN}

Substitute LN= 3PN

\frac{LM}{PQ} = \frac{3PN}{PN}

\frac{LM}{PQ} = 3

LM = 3PQ

Area of LQM is:

Area = \frac{1}{2} * LM * LP

This gives:

Area = \frac{1}{2} * 3PQ * LP

Area = 3 *\frac{1}{2} *PQ * LP

Recall that:

16= \frac{1}{2} * PQ * LP

So:

Area = 3 *16

Area = 48cm^2

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