Question

sides of a triangle are in ratio 13:14:15 and its perimeter is 21 cm find the area of triangle​

Answer 1

Perimeter of the triangle = 168 cm

Sum of ratios of sides = 15 + 13 + 14 = 42

Let the first side = (168 × 15)/42 = 60 cm

Second side = (168 × 13)/42 = 52 cm

Third side = (168 × 14)/42 = 56 cm

Now, s = (a + b + c)/2

= (60 + 52 + 56)/2 = 168/2 = 84



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Find the area of a right-angled triangle whose hypotenuse is 13 cm long and

Answer 2

$\huge \underline \mathfrak {solution : - }$

Let the sides of the triangle be 13a, 14a and 15a respectively.

Sum of all sides= perimeter of triangle

=>13a+14a+15a=42a

Given,

Perimeter of triangle=21cm

∴42a=21cm

$= > a = \frac{21}{42} = 0.5$

Now

13a=13x0.5=6.5cm

14a=14x0.5=7cm

15a=15x0.5=7.5cm

Applying Heron's Formula

$s = \frac{6.5 + 7 + 7.5}{2} = \frac{21}{2} = 10.5$

Area of the triangle

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

$= \sqrt{10.5(10.5 - 6.5)(10.5 - 7)(10.5 - 7.5)}$

$= \sqrt{10.5 \times 4 \times 3.4 \times 3}$

$= \sqrt{10.5 \times 2 \times 2 \times 3.5 \times 3}$

$= \sqrt{10.5 \times 3.5 \times 3} \: \: \: \times 2$

$= \sqrt{110.25} \times 2$

$= 6.5$

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