Question : The sides of a triangle are of length 8 cm, 15 cm, and 17 cm. Find the area of the triangle.
Option 1: 65 cm2
Option 2: 75 cm2
Option 3: 60 cm2
Option 4: 70 cm2
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Correct Answer: 60 cm 2
Solution :
The sides are 8 cm, 17 cm, and 15 cm.
Let $a=8,b=17,$ and $c=15$
Semi perimeter, $s=\frac{a+b+c}{2}=\frac{8+17+15}{2}=20$
Area of the triangle by Heron's Formula,
Area of the triangle $= \sqrt{s(s−a)(s−b)(s−c)}$
⇒ Area of the triangle $= \sqrt{20(20−8)(20−17)(20−15)}$
⇒ Area of the triangle $= \sqrt{20 \times 12 \times 3\times 5}$
⇒ Area of the triangle $= 4 \times 5 \times 3$
$\therefore$ Area of the triangle $= 60$ cm
2
Hence, the correct answer is 60 cm
2
.
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