Question

If the sides of a triangle are I the ratio 5 is to 4 is to 3.and its area is 54cm2.Find perimeter.

Answer 1

Answer:

36 cm

Step-by-step explanation:

Let the sides be 5x , 4x , 3x  i.e. pythagorean triplet

∴ It is a right angled triangled .

∴ Area = 1/2 × base × height

∴ 54 = 1/2 × 4x × 3x

∴ 108 = 12x²

∴ 9 = x²

∴ x = 3

So , the sides are :  5x = 15cm , 4x= 12cm  ,  3x =9cm

∴ Perimeter = 15 + 12 + 9 = 36cm.

Answer 2

Step-by-step explanation:

Let the sides a,b& c be the sides of the triangle

a = 5y

b = 4y

c = 3y

s = (a+b+c)/2

s = (5y+4y+3y)/2

s = 12y/2

s. = 6y

Area of triangle = 54 cm2

√s(s-a)(s-b)(s-b)(s-c) = 54

√6y(1y)(2y)(3y) = 54

6y^2 = 54

y^2 = 54/6

y^2 = 9

y = √9

y = 3 cm

a = 5×3 = 15 cm

b = 4×3 = 12 cm

c = 3×3 = 09 cm

Perimeter of the triangle = (15+12+09)cm

= 36 cm

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