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Area of a triangle are in the ratio 15:20:25 .Its perimeter is 560cm .Find its area.


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Answer 1

QUESTION:-

Area of a triangle are in the ratio 15:20:25. Its perimeter is 560cm. Find its area.

GIVEN:-

Ratio of sides of the triangle and its perimeter.

SOLUTION:-

By using Heron’s formula, we can calculate the area of a triangle.

Heron's formula for the area of a triangle is: Area =

$\sqrt{s(s - a)(s - b)(s - c)}$

Where a, b, and c are the sides of the triangle, and s = Semi-perimeter = Half the perimeter of the triangle

Where a, b, and c are the sides of the triangle, and s = Semi-perimeter = Half the perimeter of the triangleSince the ratios of the sides of the triangle are given as 15:20:25

:25So, we can assume the length of the sides of the triangle as 12x cm, 17x cm, and 25x cm.

SO:-

The perimeter of the triangle will be:-

Perimeter = 15x + 20x + 25x

• 15x + 20x + 25x = 560 (given)

• 60x = 560

• x = 540x = 560/60

• x = 9.333333 cm(Approximately 9 cm)

Therefore, the sides of the triangle:-

• 15x = 15 × 9 = 135 cm, 20x = 20 × 9 = 180 cm, 25x = 25 × 9 = 225 cm

• a = 135 cm, b = 180 cm, c = 225 cm

Semi-perimeter(s) = 560/2 = 280 cm

THEREFORE:-

By using Heron’s formula,

• Area of a triangle

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

$= \sqrt{280(280 - 135)(280 - 180)(280 - 225}$

$= \sqrt{280 \times 145 \times 100 \times 55}$

= √223,300,000

= 14943.22589

ANSWER:-

AREA OF THE TRIANGLE = 14943.22589 cm²