Question

The perimeter of the triangular field is 540m and its sides are in the ratio 25 : 17: 12. Find the area of the triangle.
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Answer 1

Answer:

900 √15 sq m

Step-by-step explanation:

Let the sides be 25x, 17x, and 12x.

Perimeter 540m

we know that the perimeter of a triangle is sum of all it's sides...

therefore

A/C

(25+17+12)x = 540m

54x = 540

x= 540/54

x=10

thus the sides are :-

250m, [ 25×10]

170m, [ 17×10 ]

and 120 [ 12×10 ]

now the sides can be found using heron's formula.

semi perimeter = 540/2

that's 270.

$\sqrt{270 \times (270 - 250) \times (270 - 170) \times (270 - 120)}$

that can be simplified as

√ (27×10) × (30) × (100) × (150)

√ (3×3×3×10) × (3×10) × (10×10) × (15×10)

√ 9 × 9 × 100 × 100 × 15

[by simplifying things]

now we can write these as

9 × 100 √15

900 √15 sq m

hope this helps.

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