Question

LMN is a right-angled triangle.
Angle NLM = 90°
PQ is parallel to LM.
The area of triangle PNQ is 8 cm2
The area of triangle LPQ is 16 cm2
Work out the area of triangle LQM.
Your final answer must begin: Area of LQM =​

Answer 1

Answer:48 cm

Step-by-step explanation:

Answer 2

The area of the triangle LQM with all the given parameters is;

Area of ΔLQM = 48 cm²

We are given;

∠ NLM = 90°

PQ ║ LM

Area of ΔPNQ = 8 cm²

Area of ΔLPQ = 16 cm²

We want to find the area of ΔLQM

Let LN = a

Let PN = b

Thus; LP = a - b

Let LM = c

Let PQ = d

Formula for area of a triangle is;

A = ¹/₂ × base × height

Thus, plugging in the relevant values;

¹/₂(bd) = 8

bd = 16  ---(eq 1)

Also;

¹/₂(a - b)d = 16 ---(eq 2)

Thus;

bd = ¹/₂(a - b)d

d will cancel out to give;

2b = a - b

a = 3b

Since LP = a - b

Then LP = 3b - b

LP = 2b

Now, by similar triangles, we can say that;

LM/PQ = LN/PN

Thus;

c/d = a/b

Since a = 3b, then;

c/d = 3b/b

c = 3d

Area of ΔLQM =  ¹/₂(LM × PL) = ¹/₂(3d × 2b)

From eq(1), we have; bd = 16

Thus; d = 16/b

Area of ΔLQM = ¹/₂(3 × (16/b) × 2b)

Area of ΔLQM = 48 cm²

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