Question

The sides of a triangle are in the ratio 3 is to 4 is to 5 its area is 54 square units find the sides

Answer 1

Answer:

sides of the triangle are

9cm, 12cm and 15cm

Step-by-step explanation:

the ratio of side of triangle = 3:4:5

area = 54 sq cm

let the sides be 3x, 4x, 5x

when sides are given we need to use herons formula

$s = \frac{3x + 4x + 5x}{2} \\ = \frac{12x}{2} = 6x \\ area \: = \sqrt{s(s - a)(s - b)(s - c)} \\ 54 = \sqrt{6x(6x - 3x)(6x - 4x)(6x - 5x)} \\ 54 = \sqrt{6x \times 3x \times 2x \times x} \\ 54 = \sqrt{36 {x}^{4} } \\ 54 = 6 {x}^{2} \\ {x}^{2} = \frac{54}{6} \\ {x}^{2} = 9 \\ x = \sqrt{9} \\ x = 3$

therefore the sides are

3x = 3×3 = 9

4x = 4×3 = 12

5x = 5×3 = 15

hope you get your answer