Question

The sides of a triangle are in the ratio 21x, 13x and 18x and its

perimeter is 182 cm. Find the area of the triangle.
​

Answer 1

Step-by-step explanation:

21x + 13x + 18x = 182

52x = 182

x = 3.5

a = 21×3.5=73.5

b= 13×3.5=45.5

c= 18×3.5=63

So these are the sides.Now u can use herons formula to find the area.You know herons formula..right??

a+b+c=s

root of s×(s-a)(s-b)(s-c)

Do the rest. Good luck

Answer 2

Solution

Given :-

• All Side of triangle = 21x , 13x , 18x
• Perimeter is = 182 cm

Find :-

• Area of triangle

Explanation

Using Formula

$\dag{\boxed{\underline{\tt{\orange{\: Perimeter_{Triangle}\:=\:Sum\:of\:all\:side}}}}}$

Now,

➠ Perimeter of triangle = 182

➠ (21x) + ( 13x) + (18x) = 182

➠ 52x = 182

➠ x = 182/52

➠ x = 14/4

➠x = 7/2

➠ x = 3.5 cm

Since

All side of triangle be

• First side (21x) = 21 × 3.5 = 73.5 cm
• Second side (13x) = 13 × 3.5 = 45.5 cm
• Third side (18x) = 18 × 3.5 = 63 cm

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For Area of Triangle,

By Heroen Feron's Formula

★Semi perimeter (S) = (Sum of all side of triangle)/2

Here, let

ABC be a triangle ,

where,

• AB = 73.5 cm
• BC = 45.5 cm
• CA = 63 cm

Then,

➠ S = (73.5 + 45.5 + 63)/2

➠S = 182/2

➠S = 91 cm

Area of triangle

★ Area = √[S(S-AB)(S-BC)(S-CA)]

Keep all above Values,

➠ Area = √[91(91-73.5)(91-45.5)(91-63)]

➠Area = √[91 × 17.5 × 45.5 × 27]

➠ Area = √(1,95,6386.25)

➠Area = 1398.56 cm²

Hence

• Area of triangle will be = 1398.56 cm²

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