5. Find the area of the triangle whose sides are 20 cm, 30 cm, and 40 cm.
Answers
Step-by-step explanation:
AccordingtotheQuestion
Assumption
∆PQR are the sides of triangle.
P = 20 cm
Q = 30 cm
R = 40 cm
Now,
Perimeter of ∆ = (P + Q + R)
= (20 + 30 + 40)
= 90
Semi perimeter
{\boxed{\sf\:{s=\dfrac{P+Q+R}{2}}}}
s=
2
P+Q+R
\tt{\rightarrow\dfrac{90}{2}}→
2
90
= 45 cm
Using Herons Formula
{\boxed{\sf\:{Area\;of\; \triangle=\sqrt{s(s-a)(s-b)(s-c)}}}}
Areaof△=
s(s−a)(s−b)(s−c)
\tt{\rightarrow\sqrt{45(45-20)(45-30)(45-40)}}→
45(45−20)(45−30)(45−40)
\tt{\rightarrow\sqrt{45\times 25\times 15\times 5}}→
45×25×15×5
\tt{\rightarrow\sqrt{3^2\times 5\times 5^2\times 3\times 5\times 5}}→
3
2
×5×5
2
×3×5×5
\tt{\rightarrow\sqrt{3^2\times 5^2\times 5^2\times 5\times 3}}→
3
2
×5
2
×5
2
×5×3
\tt{\rightarrow 3\times 5\times 5\sqrt{15}}→3×5×5
15
\tt{\rightarrow 75\sqrt{15}}→75
15
= 75 × 3.8729
= 290.47 cm²
Area of Triangle = Sum of all sides
= 20 + 30 + 40
= 90 cm²