How many districts are in India which are administered by their respective state/UT Governments??
Answers
Answer:
Given -
Sides of three triangles.
To find -
Area of triangles.
Formula used -
Heron's formula
Solution -
In the question, we are provided with the sides of 3 triangles, and we need to find it's area. For that, we will apply heron's formula and will find every triangle's area. For that, first we will add up side a , b and c and then, semi - perimeter and then applying heron's formula, we will find their area
Let's do it!
Heron's formula says -
\begin{gathered} \sf \: \sqrt{s \:(s \: - a)(s \: - b)(s \: - c)} \\ \end{gathered}
s(s−a)(s−b)(s−c)
For 1st triangle -
Side a = 9 cm
Side b = 10 cm
Side c = 17 cm
Semi - Perimeter -
\begin{gathered} \sf \: s \: = \dfrac{9 \: + \: 10 \: + \: 17}{2} \\ \\ \sf\: s \: = \cancel\frac{36}{2} \\ \\ \sf\: s \: = 18\end{gathered}
s=
2
9+10+17
s=
2
36
s=18
Area of 1st triangle -
\begin{gathered} \sf \sqrt{18(18 \: - \: 9)(18 \: - \: 10)( 18\: - \: 17)} \\ \\ \sf \: \sqrt{18 \: \times \: 9 \: \times \: 8 \: \times \: 1} \\ \\ \sf \: \sqrt{1296} \\ \\ \sf \: 36 { \: cm}^{2} \\ \end{gathered}
18(18−9)(18−10)(18−17)
18×9×8×1
1296
36cm
2
For 2nd triangle -
Side a = 13 cm
Side b = 5 cm
Side c = 12 cm
Semi - Perimeter -
\begin{gathered} \sf \: s \: = \dfrac{13 \: + \: 5 \: + \: 12}{2} \\ \\ \sf \: s \: = \cancel \dfrac{30}{2} \\ \\ \sf \: s \: = 15 \\ \end{gathered}
s=
2
13+5+12
s=
2
30
s=15
Area of 2nd triangle -
\begin{gathered} \sf \: \sqrt{15(15 \: - \: 13)(15 \: - \: 5)(15 \: - \: 12)} \\ \\ \sf \: \sqrt{15 \: \times 2 \: \times \: 10 \: \times \: 3} \\ \\ \sf \: \sqrt{900} \\ \\ \sf \: 30 { \: cm}^{2} \end{gathered}
15(15−13)(15−5)(15−12)
15×2×10×3
900
30cm
2
For 3rd triangle -
Side a = 35 m
Side b = 45 m
Side c = 50 m
Semi - perimeter -
\begin{gathered} \sf \: s \: = \dfrac{35 \: + \: 45 \: + \: 50}{2} \\ \\ \sf \: s \: = \cancel\frac{130}{2} \\ \\ \sf \: s \: = 65 \\ \end{gathered}
s=
2
35+45+50
s=
2
130
s=65
Area of 3rd triangle -
\begin{gathered} \sf \: \sqrt{65(65 \: - \: 35)(65 \: - \: 45)(65 \: - \: 50)} \\ \\ \sf \: \sqrt{65 \: \times \: 30 \: \times \: 20 \: \times \: 15} \\ \\ \sf \: \sqrt{585000} \\ \\ \sf \: 764.8 \: m^{2} \: (appox) \\ \end{gathered}
65(65−35)(65−45)(65−50)
65×30×20×15
585000
764.8m
2
(appox)
718 Districts
There are 718 Districts in India administered by their respective State/ UT Government.