Question

the area of atriangle is 150 cm square and its sides are in the ratio 3:4:5.ehat is its perimeter​

Answer 1

Step-by-step explanation:

given the area= 150

sides ratio = 3:4:5

clearly the ratio of sides justify that the triangle is a right angled triangle

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

then are = (1/2)× 3x×4x= 150

= x^2 = 150×2/12

x^2= 25

x= 5

perimeter

= (3+4+5)×5

= 12×5

= 60 cm

Answer 2

Given :

• Area of Triangle = 150cm²
• Sides of triangle are in the ratio 3:4:5.

To Find :

• Perimeter of Triangle.

Solution :

$\longmapsto\tt{Let\:1st\:Side\:be=3x}$

$\longmapsto\tt{Let\:2nd\:side\:be=4x}$

$\longmapsto\tt{Let\:3rd\:side\:be=5x}$

Now ,

$\longmapsto\tt{s=\dfrac{a+b+c}{2}}$

$\longmapsto\tt{s=\dfrac{3x+4x+5x}{2}}$

$\longmapsto\tt{s=\cancel\dfrac{12x}{2}}$

$\longmapsto\tt\bold{s=6x}$

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

$\longmapsto\tt{150=\sqrt{6x(6x-3x)(6x-4x)(6x-5x)}}$

$\longmapsto\tt{150=\sqrt{6x\times{3x}\times{2x}\times{1x}}}$

$\longmapsto\tt{150=\sqrt{3x\times{2x}\times{3x}\times{2x}\times{1x}}}$

$\longmapsto\tt{150=\sqrt{3x\times{2x}}}$

$\longmapsto\tt{150=\sqrt{6{x}^{2}}}$

$\longmapsto\tt{\cancel\dfrac{150}{6}={x}^{2}}$

$\longmapsto\tt{\sqrt{25}=x}$

$\longmapsto\tt\bold{x=5}$

Therefore ,

$\longmapsto\tt{1st\:Side=3(5)}$

$\longmapsto\tt\bold{15cm}$

$\longmapsto\tt{2nd\:Side=4(5)}$

$\longmapsto\tt\bold{20cm}$

$\longmapsto\tt{5(5)}$

$\longmapsto\tt\bold{25cm}$

Now ,

$\longmapsto\tt{a=15cm\:,\:b=20cm\:,\:c=25cm}$

Using Formula :

$\longmapsto\tt\boxed{Perimeter\:of\:Triangle=a+b+c}$

Putting Values :

$\longmapsto\tt{15+20+25}$

$\longmapsto\tt\bold{60{cm}^{2}}$

So , The perimeter of triangle is 60cm²..