Question

Q1 If the lengths of the sides of a
triangle are in the ratio 3: 4:5 and its
perimeter is 48 cm. find its area. *​

Answer 1

Answer:

Semiperimeter = 48/2 = 24 CM. = 96 cm². Let the sides be 3x , 5x , 7x . Therefore, the sides are 60 ,100 , 140m

Answer 2

Given :

• Sides of Triangle are in the ratio 3:4:5

To Find :

• Area of Triangle.

Solution :

• a = 3x
• b = 4x
• c = 5x

$\longmapsto\tt{3x+4x+5x=48}$

$\longmapsto\tt{12x=48}$

$\longmapsto\tt{x=\cancel\dfrac{48}{12}}$

$\longmapsto\tt\bf{x=4}$

Value of x is 4..

Therefore :

$\longmapsto\tt{First\:Side(a)=3(4)=12cm}$

$\longmapsto\tt{Second\:Side(b)=4(4)=16cm}$

$\longmapsto\tt{Third\:Side(c)=5(4)=20cm}$

Now ,

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

$\longmapsto\tt{s=\dfrac{12+16+20}{2}}$

$\longmapsto\tt{s=\cancel\dfrac{48}{2}}$

$\longmapsto\tt\bf{s=24cm}$

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

$\longmapsto\tt{\sqrt{24(24-12))(24-16)(24-20)}}$

$\longmapsto\tt{\sqrt{24(12)(8)(4)}}$

$\longmapsto\tt\sqrt{{2\times{2}\times{3}\times{2}\times{2}\times{2}\times{3}\times{2}\times{2}\times{2}\times{2}\times{2}}}$

$\longmapsto\tt{2\times{2}\times{2}\times{2}\times{2}\times{3}}$

$\longmapsto\tt\bf{96{cm}^{2}}$

So , The Area of Triangle is 96cm²..