The sides of a triangular plot are in the ratio 3: 5: 7; its perimeter is 300 m. Find its area.
Answer: Sides 60 m, 100 m, 140 m; s = 150. Area = √(150 × 90 × 50 × 10) = √6 750 000 = 1500√3 ≈ 2598 m2.
Step-by-step solution
Given: Sides in the ratio 3 : 5 : 7; Perimeter = 300 m
To find: Area of the plot
To find: Area of the plot
Idea: Write the sides as 3x, 5x, 7x, find x from the perimeter, then apply Heron’s formula.
- 3x + 5x + 7x = 300 ⇒ 15x = 300 ⇒ x = 20. Sides: 60 m, 100 m, 140 m.1 mark
- s = 150 m; s − a = 90, s − b = 50, s − c = 10.½ mark
- Area = √(150 × 90 × 50 × 10) = √6 750 000 = √(2 250 000 × 3) = 1500√3 ≈ 1500 × 1.732 = 2598 m2.1½ marks
Area of the plot = 1500√3 m² ≈ 2598 m².
Check: 1500√3 = 2598.08…, and (2598.08)2 ≈ 6 750 000 ✓.
Answer to write in the exam
3x + 5x + 7x = 300 ⇒ x = 20
Sides: 60 m, 100 m, 140 m; s = 150 m
Area = √(150 × 90 × 50 × 10)
= √6750000 = 1500√3
∴ Area ≈ 2598 m2
Common mistakes that cost marks
- Using 300 ÷ 3 = 100 as the multiplier. Divide by 3 + 5 + 7 = 15.
- Using s = 300.
- Arithmetic slips in the big product; factor first: 150 × 90 × 50 × 10 = 15002 × 3.
How this can come in the exam
MCQ (1 mark)
The sides of a triangle are in the ratio 5 : 12 : 13 and its perimeter is 60 cm. Its area is
- 60 cm2
- 130 cm2
- 240 cm2
- 120 cm2
Show answer
(D) 120 cm2
x = 2: sides 10, 24, 26 (right-angled). Area = 12 × 10 × 24 = 120 cm2.
Try one yourself
The sides of a triangle are in the ratio 13 : 14 : 15 and its perimeter is 84 cm. Find its area.
Show answer
x = 2: sides 26, 28, 30; s = 42; √(42 × 16 × 14 × 12) = √112896 = 336 cm2.
More questions like this
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