Question

Find the area of triangle whose side are 14, 15cm17cm

Answer 1

Let the sides of triangle be a, b and c
For, area of triangle,semiperimeter=a+b+c/2
=15+14+17/2
=46/2
=23cm
Area of triangle=√s(s-a)(s-b)(s-c)
=√23(23-15)(23-14)(23-17)
=√23×8×9×6
=√23×2×2×2×3×3×3×2
=12√23×3
=12√69cm^2
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Answer 2

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\therefore{\text{Area\:of\:triangle=99.67\:cm}^{2}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{ \underline \bold{Given : }} \\ : \implies \text{Sides \: of \: triangle =14 cm,15 cm,17 cm} \\ \\ \red{ \underline \bold{To \: Find : }} \\ : \implies \text{Area \: of \: triangle = ?}$

• According to given question :

$\bold{As \: we \: know \: that \: herons \: formula} \\ : \implies s = \frac{a + b + c}{2} \\ \\ : \implies s = \frac{14+15+17}{2} \\ \\ : \implies s = \frac{46}{2} \\ \\ \green{ : \implies s =23 } \\ \\ \circ\: \bold{Area \: of \: triangle = \sqrt{s(s - a)(s - b)(s - c)} } \\ \\ : \implies \text{Area \: of \: triangle =} \sqrt{23(23- 14)(23-15)(23- 17)} \\ \\ : \implies \text{Area \: of \: triangle =}\sqrt{23\times 9\times8\times 6} \\ \\ : \implies \text{Area \: of \: triangle =} \sqrt{9936} \\ \\ : \implies \text{Area \: of \: triangle =}99.67\: cm^{2} \\ \\ \ \green{\therefore \text{Area \: of \: triangle =99.67\: {cm}}^{2} }$