Question

If the semi perimeter of an equilateral triangle is 54 cm than find length of each side.​

Answer 1

$\mathbb{QUESTION}$

$\text{If the semi perimeter of an equilateral triangle is 54 cm than find length of each side.​}$

$\mathbb{SOLUTION}$

$\boxed{\boxed{\textsf{Perimeter}}}$

The total boundary of a shape is called perimeter

for triangle      $A+B+C$ $\text{-where A,B,C are the sides of triangle}$

for rectangle  $2(L+B)$$\text{-where L-length,B-breadth}$

for square       $4S$ $\text{-where S-side}$

$\boxed{\boxed{\textsf{Semi -perimeter}}}$

Semi perimeter is the half of perimeter which is

for triangle      $\frac{a+b+c}{2}$

for rectangle  $\frac{2(L+B)}{2}=L+B$

for square       $\frac{4S}{2}=2S$

$\mathbf{Given}$-

Semi-perimeter of equilateral triangle is 54cm

$\frac{a+b+c}{2}$$= 54$

$a+b+c=54 \times 2$

$a+b+c=108$

$\mathbf{To \:find}$ -length of equilateral triangle-

In △ABC, ∠B=∠C - $\mathbf{Given}$

Construct AF←→, the angle bisector of ∠A, with  the intersection of  and .

-

∠BAF=∠CAF  -$\textbf{An angle has only one angle bisector}$

AF=AF -$\mathbf{Reflexive \:Property}$

ΔABF≅ΔACF  -$\textbf{AAS congruence rule}$

AB=AC -

$\therefore$ Through the proof the sides of equilateral triangle are equal .

$P=A+B+C$

$P=3S$$\to \textsf{since sides of equilateral triangle are equal P=3S}$

$108=3S$

$3S=108$

$S=\frac{108}{3}$

$S=36$

$\boxed{S=36}$

which means the length of equilateral triangle =36

$\mathcal{HOPE\:IT\:HELPS}$

$\mathcal{BY\;BRAINLY\:ROSHAN}$

Answer 2

Answer:

Step-by-step explanation:

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