Question

find the area of a triangle two sides of which are 8cm and 11cm and the perimeter is 30cm​

Answer 1

QUESTION

Find the area of a triangle two sides of which are 8cm and 11cm and the perimeter is 32cm

Solution:

Let a,b,c be the sides of the given triangle such that

perimeter of triangle = 32cm

a=8 cm, b=11 cm c=?

• a+b+c= perimeter of triangle
• 8+11+c=32
• c=32-21
• c=13cm

a=8 cm, b=11 cm c=13 cm

perimeter of triangle = 32cm

semi perimeter= $\dfrac{perimeter of triangle}{2}$

semi perimeter= $\dfrac{32}{2}$

semi perimeter= $\bold{15 cm}$

Hence, area of given triangle=

$\sqrt{s(s - a)(s - b)(s - c)} \\ \sqrt{16(16 - 8)(16 - 11)(16 - 13)} \\ \sqrt{16 \times 8 \times 5 \times 3} \\ \sqrt{16 \times 8 \times 15} \\ \sqrt{16 \times 120} \\ \sqrt{2^{4 + 3} \times 3 \times 5} \\ \sqrt{{2}^{6} \times 2 \times 3 \times 5} \\ \sqrt{ {2}^{6} } \times \sqrt{2 \times 3 \times 5} \\ {2}^{ \frac{6}{2} } \times \sqrt{2 \times 3 \times 5 } \\ {2}^{3} \times \sqrt{2 \times 3 \times 5} \\ 8 \sqrt{30}$

area of triangle in cm = $8 \sqrt{30}$

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FOR MORE INFORMATION

• Perimeter of a Rectangle = 2 (l + b)
• Area of a Rectangle = L×B