Question

The lengths of sides of a triangle are in the ratio 3: 4:5 and its perimeter is 120 cm.
find its area​

Answer 1

Step-by-step explanation:

Let the side of the trianle be x

therefore, all the sides are

3x, 4x, 5x

therefore, according to the give condition

3x + 4x + 5x = 120 (as perimeter of the triangle is sum of all the sides

12x = 120

x = 10

sides

30 . 40 ,50

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Answer 2

❍Let the sides be 3x,4x and 5x and perimeter is 120 cm respectively.

Let us use the heron's formula here,

• Perimeter ; 2s = a + b + c

Applying the values,

$\: \: \: \: \: \: \: \: : \implies \sf{120 = 3x + 4x + 5x }\\ \\ \: \: \: \: \: : \implies \sf{120= 12x }\\ \\ \: \: \: \: \: \: \: \: \: \: \: : \implies \sf{ x = 120 ÷ 12} \\ \\ \: \: \: \: \: \: : \implies \sf{ x = 10 \: cm }$

• Therefore,The value of x is 10 cm,

Putting the value of x in the given sides,

$\to \mathfrak{3x = 3 \times 10 = 30 \: cm} \\ \\ \to\mathfrak{4x = 4 \times 10 = 40 \: cm} \\ \\ \to\mathfrak{5x = 5 \times 10 = 50 \: cm}$

• So,The sides is 30 cm,40 cm and 50 cm.

$\: \: \: \: \implies \sf{2s = a + b + c} \\ \\ \: \: \: \: \implies \sf{2s = 30 + 40 + 50} \\ \\ \: \: \: \: \implies \sf{2s = 120} \\ \\ \: \: \: \: \implies \sf{s = \cancel{\frac{120}{2}}} \\ \\ \: \: \: \: \implies \sf{s = 60 \:cm}$

• Here,The value of s is 60 cm.

$\sf{Area \: of \: triangle = \sqrt{s(s - a)(s - b)(s - c)}} \\ \\ \rm{putting \: the \: values} \\ \\ \sf{A = \sqrt{60(60 - 30)(60 - 40)(60 - 50)}} \\ \\ \sf{A = \sqrt{60(30)(20)(10)}} \\ \\ \sf{A = \sqrt{2 \times 30 \times 30 \times 2 \times 10 \times 10}} \\ \\ \sf{A = \sqrt{{2}^{2} \times {30}^{2} \times {10}^{2}}} \\ \\ \sf{A = 2 \times 30 \times 10} \\ \\ \sf{A = 600 \: {cm}^{2}}$

• Therefore,The area of triangle is 600 cm².

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