Question

The area of a triangle is 150 cm2 and its sides are in the ratio 3 : 4 : 5. What is its perimeter?The area of a triangle is 150 cm2 and its sides are in the ratio 3 : 4 : 5. What is its perimeter?

Answer 1

The area of triangle = 150 cm²

Let all the sides be x

Side a = 3x

Side b = 4x

Side c = 5x

Side a + Side b + Side c = 180° (Angle sum property)

3x + 4x + 5x = 180°

12x = 180

x = 180/12

x = 15

Side a = 3x

= 3 × 15

= 45 cm

Side b = 4x

= 4 × 15

= 60 cm

Side c = 5x

= 5 × 15

= 75 cm

Now,

Perimeter of triangle = a + b + c

= 45 + 60 + 75

= 180 cm

Hope it helps :)

Answer 2

Answer:

Step-by-step explanation:

Let the sides be,

a= 3$x$

b= 4$x$

c =5$x$

s = a+b+c/2

    3$x$+4

    12$x$/2

    6$x$

   

√[s(s-a)(s-b)(s-c)]

√6$x$ (6$x$ - 3$x$) (6$x$-

√6$x$×3

√36$x^{4}$

6$x^{2}$ will be the area

So now,

6$x^{2}$ = 150

$x^{2}$ = 150/6

$x^{2}$ = 25

$x$ = √25

$x$ = 5

3$x$ = 3*5 = 15

4$x$ = 4*5 = 20

5$x$ = 5*5 = 25

So perimeter will be,

15+20+25

60

∴ The perimeter is 60cm