Question

Find the area of a triangle, two sides of which are 8 cm and 11 cm and the perimeter is 32 cm.

My answer is not able to match the options given, please some one help me with this problem.
My weird answer: 8(um... where is the under root sign....)_/30
(its 8 under root 30)​

Answer 1

$\huge\rm\underline\pink{Solution:-}$

Given sides are 8cm , 11cm

Let another side be 'c'

Perimeter of triangle = 32 cm

$\large\rm\bold{\boxed{Perimeter\:of\:triangle\:=\:(a+b+c)}}$

$\large\rm{a,b,c\rightarrow{Sides\:of\:triangle}}$

$\large\rm{\implies{a+b+c\:=\:32}}$

$\large\rm{\implies{8+11+c\:=\:32}}$

$\large\rm{\implies{c\:=\:13\:cm}}$

By using Heron's Formula ,

$\large\rm\bold{\boxed{Area\:of\:triangle\:=\:\sqrt{s(s-a)(s-b)(s-c)}}}$

$\large\rm{s\rightarrow{Semiperimeter}}$

$\large\rm{a,b,c\rightarrow{Sides\:of\:triangle}}$

$\large\rm{Semiperimeter\:=\:\frac{a+b+c}{2}}$

$\large\rm{\implies{Semiperimeter\:=\:16\:cm}}$

$\large\rm{Area\:of\:Triangle\:=\:\sqrt{16(16-8)(16-11)(16-13)}}$

$\large\rm{\implies{Area\:of\:Triangle\:=\:\sqrt{16(8)(5)(3)}}}$

$\large\rm{\implies{Area\:of\:triangle\:=\:8\sqrt{30}}}$

∴ Area of triangle = 8√30 sq.m

Answer 2

the answer is 8 root 30

just think about it, how cud the are of a triangke of 8,11 and 13 cm be more than 1000