Question

If the sides of a triangle are in the ratio 8:4:6 and its perimeter is 72 cm, find the area of the triangle​

Answer 1

Given :-

• Sides of a triangle are in the ratio 8:4:6
• its perimeter is 72 cm

To Find :-

• Area of triangle

Solution :-

Let the sides of triangle be 8x , 4x and 6x

Perimeter = 72cm

Also, Perimeter = sum of all sides

A.T.Q.

Perimeter = sum of all sides

➙ 72cm = 8x + 4x + 6x

➙ 72cm = 18x

➙ x = $\dfrac{72}{18}$

➙ x = $\dfrac{\cancel{72}}{\cancel{18}}$

✯ x = 4

∴ Side are :-

8x = 8 × 4 = 32cm

4x = 4 × 4 = 16cm

6x = 6 × 4 = 24cm

Now,

Sides of triangle Area = 32cm , 16cm , 24cm

So we can say that :-

A = 32cm

B = 16cm

C = 24cm

$\mathtt{\boxed{Semi\:perimeter\:=\: \dfrac{Sum\:of\:all\:sides}{2}}}$

$\mapsto{\bold{Semiperimeter\:=\: \dfrac{32+16+24}{2}}}$

$\mapsto{\bold{Semiperimeter\:=\: \dfrac{72}{2}}}$

$\mapsto{\large{\bold{Semiperimeter\:=\: 36\:cm}}}$

$\large{\bold{Area\:=\: \sqrt{s(s-a)(s-b)(s-c)}}}$

${\bold{Area\:=\: \sqrt{36(36-32)(36-16)(36-24)}}}$

${\bold{Area\:=\: \sqrt{36(4)(20)(12)}}}$

${\bold{Area\:=\:\sqrt{2×2×3×3×2×2×2×2×5×2×2×3}}}$

${\bold{Area\:=\: 2×2×2×2×3\sqrt{5×3}}}$

$\huge{\mathtt{\red{Area\:of\:triangle\:=\:48\sqrt{15}}}}$