Find the area, to the nearest cm², of the triangle whose sides are in the ratio 2 : 3 : 4 and whose perimeter is 180 cm.

Correct Answer is : 1162 cm2²2

Correct Answer is : 1162 cm2²2

Test Index

JAMB Mathematics 2023 Paper

Question : 47

Total: 80

^{2}

Solution:

Concept:

Use the given ratio to find the real side lengths, then apply Heron’s formula to calculate the area.

Explanation:

Let the sides be

2x

3x

, and

4x

The perimeter is

180\text{ cm}

, so:

2x + 3x + 4x = 180

9x = 180

x = 20

Therefore, the side lengths are:

2x = 40\text{ cm},\quad 3x = 60\text{ cm},\quad 4x = 80\text{ cm}

Find the semi-perimeter,

s

s = \frac{40 + 60 + 80}{2} = 90\text{ cm}

Using Heron’s formula:

A = \sqrt{s(s-a)(s-b)(s-c)}

A = \sqrt{90(90-40)(90-60)(90-80)}

A = \sqrt{90 \times 50 \times 30 \times 10}

A = \sqrt{1,350,000} \approx 1161.895

To the nearest

\text{cm}^2

, the area is

1162\text{ cm}^2

Answer:

1162\text{ cm}^2

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