Question

The sides of a triangle are 16 cm, 30 cm, 34 cm. Its area is​

Answer 1

Answer:

240 cm²

Step-by-step explanation:

The sides are - 16 cm, 30 cm, 34 cm

Therefore we can say it's a Scalene Triangle.

Formula of Area of Scalene Triangle =

$\sqrt{s(s - a)(s - b)(s - c)}$

Where s =

$\frac{perimeter}{2}$

& a, b and c are the sides....

So,

$s = \frac{16 + 30 + 34}{2} = \frac{80}{2} cm = 40 \: cm$

Area =

$\sqrt{40(40 - 16)(40 - 30)(40 - 34)}$

$= \sqrt{40 \times 24 \times 10 \times 6}$

Now break every number into Prime Factors.

= √ 2×2×2×5×2×2×2×3×2×5×2×3

Now pair all the similar numbers

$\sqrt{ {2}^{2} \times {2}^{2} \times \: {2}^{2} \times {2}^{2} \times {3}^{2} \times {5}^{2} }$

$= 2 \times 2 \times 2 \times 2 \times 3 \times 5$

$= 16 \times 15$

$= 240 \: \: {cm}^{2}$

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Answer 2

So, the answer is 240 cm^2