Question

The sides of a triangle are in the ratio 5:12:13 and its perimeter 150 m find the area of the triangle. is​

Answer 1

☘️ Given :

• Ratio of the sides of the triangle = 5:12:13
• Perimeter = 150 m

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☘️ To find :

• Area of the triangle.

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☘️ Solution :

Let the sides of the triangle be 5x, 12x and 13x

So,

Perimeter of triangle = a + b + c

→ 5x + 12x + 13x = 150m

→ 30x = 150

→ x = 150/30

→ x = 5

So, the sides of the triangle are :

• 5x = 5 × 5 = 25
• 12x = 12 × 5 = 60
• 13x = 13 × 5 = 65

So, a = 25, b = 60 and c = 65.

$\\ \sf \purple{s \: = \: \dfrac{a + b + c}{2} } \\ \\ \sf \implies \: \dfrac{25 + 60 + 65}{2} \: \\ \\ \sf \implies \: \: \frac{150}{2} = \purple{ 75 \: m }$

Area of triangle :

• Using Heron's formula:

$\bf \pink{Area \: = \: \sqrt{s(s - a)(s - b)(s - c)}} \\ \\ \twoheadrightarrow \tt Area \: = \: \sqrt{75(75 - 25)(75 - 60)(75 - 65)} \\ \twoheadrightarrow \tt Area \: = \: \sqrt{70 \times 50 \times 15 \times 10} \\ \twoheadrightarrow\tt Area \: = \: \sqrt{25 \times 3 \times 25 \times 2 \times 5 \times 3 \times 5 \times 2} \\ \ \twoheadrightarrow\tt Area \: = \: \sqrt{25 \times 25 \times 5 \times 5 \times 3 \times 3 \times 2 \times 2} \\ \twoheadrightarrow\tt Area \: = \:25 \times 5 \times 3 \times 2 \\ \purple{\twoheadrightarrow\bf Area \: = \:750 \: sq. \: m}$

.°. Area of the triangle = 750 sq. m.

☘️ Answer :

• Area of the triangle = 750 sq. m.