Question

side of a triangle are in ratio 5 : 3 : 3 . parameters of the triangle is 110 cm find the area of the triangle
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Answer 1

According to the question,

5x + 3x + 3x = 110

11x = 110

x = $\frac{110}{11}$

x = 10

so, sides are

5x = 5 x 10 = 50

3x = 3 x 10 = 30

3x = 3 x 10 = 30

Area --->

By heron's formula

s = $\frac{50+30+30}{2}$ = 110/2 = 55

area = $\sqrt{55(55-50)(55-30)(55-30)}$

area = √{55(5)(25)(25)}

area =  √275 * 625 = 11√5*25 = 275√5cm^2

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Answer 2

Let 1st side = 5x

2nd side = 3x

3rd side = 3x

Perimeter = 110cm(given)

Sum of all sides of triangle = 110cm

5x + 3x + 3x = 110

11x = 110

x = 110/11

x = 10

Now put value to find sides,

1st side = 5x = 5×10 = 50cm

2nd side = 3x = 3×10 = 30cm

3rd side = 3x = 3×10 = 30cm

Now let 1st side, a = 50cm

2nd side, b = 30cm

3rd side, c = 30cm

semi-perimeter, s = a+b+c/2 = 50+30+30/2 = 110/2 = 55cm

By heron's formula,

Area of triangle = √s(s-a)(s-b)(s-c)

= √55(55-50)(55-30)(55-30)

= √55×5×25×25

= √5×11×5×5×5×5×5

= 5×5×5√11

= 125√11cm²

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