Question

The ratio of sides of a triangle is 3:4:5 and area of the triangle is 72 square unit. Then the area of an equilateral triangle whose perimeter is same as that of the previous triangle is

• A. $$32\sqrt{3}squnits$$
• B. $$48\sqrt{3}squnits$$
• C. 96 squnits
• D. $$60\sqrt{3}squnits$$

Answer 1

Answer:

$$48\sqrt{3}squnits$$

Sides of triangle

Let 3x, 4x and 5x units

Here, (3x)² + (4x)² = (5x)²

It is a right angled triangle.

Now, Area of triangle $=\frac{1}{2}\times{3x}\times{4x}=6x^2$

$6x^2=72$

=>x^2=12

=>x=\sqrt{12}=2\sqrt{3}

Perimeter of right angled triangle $= 3x + 4x + 5x = 12x = 12 × 2 \sqrt{3}= 24 \sqrt{3} units$

Perimeter of equilateral triangle $= 24\sqrt{3} units$

Its side $=\frac{24\sqrt{3}}{3}=8\sqrt{3}units$

$Area =\frac{\sqrt {3}}{4}\times{(side)^2}$

$=\frac{\sqrt{3}}{4}\times{8\sqrt{3}}\times{8\sqrt{3}}$

$=16\times{3}\sqrt{3}$

$=48\sqrt{3}$ sq.units