Question

The area of a triangle is 216 cm^2 and its sides are in the ratio 3 : 4 : 5. The perimeter of the triangle is what ?​

Answer 1

$\huge\underline\bold{Answer:-}$

Given that,

$area \: of \: the \: triangle \: = 216 \: cm {}^{2}$

Let the sides of the triangle be 3x, 4x and 5x cm.

$s = \frac{3x + 4x + 5x}{2} = \frac{12x}{2} = 6x$

Therefore, area of the triangle

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

$= \sqrt{6x(6x - 3x)(6x - 4x)(6x - 5x)}$

$= \sqrt{6x \times 3x \times 2x \times x } = 6 {x}^{2}$

Given,

$6x {}^{2} = 216$

$= > x {}^{2} = \frac{216}{6} = 36$

$= > x = 6$

Therefore, the sides of the triangle are (3 × 6) cm,(4 × 6) cm and (5 × 6) cm, i.e, 18 cm, 24 cm and 30 cm.

Perimeter = sum of all sides

Perimeter = 18 cm + 24 cm + 30 cm

= 72 cm.

Answer 2

$\huge\underline\mathfrak\red{✨ Answer✨}$

Clearly, 3, 4 and 5 form a triplet therefore, consider the triangle, a right triangle.

Let the sides are 3x, 4x and 5x perimeter

= 3x + 4x + 5x = 12x. Area of triangle

=12×3x×4x 12×3x×4x

=216