Q.1) Find the area of the triangle whose sides are 13cm,14cm,15cm.
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Q.1) Find the area of the triangle whose sides are 13cm,14cm,15cm.
Need a correct answer
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The following Question is a part of Application of Heron's Formula
Your Answer:
Given:-
[tex]\tt \star a = 13cm \\\\ \tt \ \star b = 14cm \\\\ \tt \star c = 15cm \\\\ \tt Where \ \ a,b \ \ and \ \ c \ \ are sides \ \ of \ \ the \ \ Triangle[/tex]
Solution:-
We know that
[tex]\tt Area \ \ of \ \ Triangle =\sqrt{s(s-a)(s-b)(s-c)} \\\\ \tt Where \ \ s \ \ is \ \ the \ \ semi-perimeter \ \ of \ \ Triangle[/tex]
So, finding 's' first
[tex]\tt s = \dfrac{a+b+c}{2} \\\\ \tt \Rightarrow s = \dfrac{13+14+15}{2} \\\\ \tt \Rightarrow s = \dfrac{42}{2} \\\\ \tt \Rightarrow s= 21[/tex]
Now replacing values of s,a,b and c
[tex]\tt Area = \sqrt{21(21-13)(21-14)(21-15)} \\\\ \tt \Rightarrow Area = \sqrt{21 \times 8 \times 7 \times 6} \\\\ \tt \Rightarrow Area = \sqrt{7\times 3 \times 4 \times 2 \times 7 \times 3 \times 2} \\\\ \tt \Rightarrow Area = 7 \times 3 \times 2 \times 2 \\\\ \tt \Rightarrow Area = 21 \times 4 \\\\ \tt \Rightarrow Area = 84cm^2[/tex]
Sp, the area of triangle is 84cm^2
Question:-
➣ Find the area of the triangle whose sides are 13cm,14cm,15cm.
AnSwER:-
➣
Given:-
➣a = 13cm
➣ b = 14cm
➣ c = 15cm
Here, a , b and c are sides of the Triangle.
Solution:-
We know:-
Heron's Formula:-
Area of Triangle =[tex]\sqrt{s(s-a)(s-b)(s-c)} [/tex]
•Finding Semi Perimeter(s):-
s =[tex] \dfrac{a+b+c}{2} [/tex]
s = [tex]\dfrac{13+14+15}{2} [/tex]
s = [tex]\dfrac{42}{2}[/tex]
s = [tex]\cancel{\dfrac{42}{2}}[/tex]
s= 21
• Replacing values of s,a,b and c:-
➣Area = [tex]\sqrt{21(21-13)(21-14)(21-15)}[/tex]
➣Area = [tex]\sqrt{21 \times 8 \times 7 \times 6}[/tex]
➣Area = [tex]\sqrt{7\times 3 \times 4 \times 2 \times 7 \times 3 \times 2}[/tex]
➣Area = [tex]7 \times 3 \times 2 \times 2[/tex]
➣Area = [tex]21 \times 4[/tex]
➣Area = [tex]84cm^2[/tex]
Therefore, the Area of Triangle is : 84cm²