Question

The lengths of three medians of a triangle are 9 cm 12 cm and 15 cm find the area of the triangle

Answer 1

a=9cm
b=12cm
c=15cm
perimeter of triangle=a+b+c=2s
2s=9+12+15
s=36/2=18
Area of triangle=androot[s(s-a)(s-b)(s-c)
=androot[18(18-9)( 18-12)( 18-15)]
=androot( 18×9×6×3)
=androot(2×3×3×3×3×2×3×3)
=androot(2×3×3×3)^2
=54cm^2

Answer 2

The area of triangle is 72 square cm

Solution:

Given that,

The lengths of three medians of a triangle are 9 cm 12 cm and 15 cm

To find: Area of triangle

The area of triangle is given as:

$\text{Area of triangle} = \frac{4}{3} \times ( \text{ Area of triangle formed by median as side })$

$\text{ Area of triangle formed by median as side } = \frac{1}{2} \times base \times height$

Therefore,

$\text{Area of triangle } = \frac{4}{3} \times \frac{1}{2} \times 9 \times 12\\\\\text{Area of triangle } = 2 \times 3 \times 12\\\\\text{Area of triangle } = 72$

Thus area of triangle is 72 square cm

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