Question

If the base of a right angled triangle is 6 cm and the hypotenuse is 10 cm, find it's area.​

Answer 1

Answer:

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Step-by-step explanation:

Height=8cm

Area=1/2×6×10=30 cm²

Answer 2

Answer:

Area of the triangle is 24cm²

Step-by-step explanation:

$\texttt{Base of triangle = 6cm}$

$\texttt{Hypotenuse of triangle = 10cm}$

$\because \mathtt{(hypotenuse)^2 =(base)^2+(height)^2}$

$\therefore \mathtt{(height)^2=(hypotenuse)^2-(base)^2}$

$\implies \mathtt{(height)^2=10^2-6^2}$

$\implies \mathtt{(height)^2=100-36}$

$\implies \mathtt{(height)^2=64}$

$\implies \mathtt{height=\sqrt{64}}$

$\implies \mathtt{height=8cm}$

Hence sides of the triangle are 6cm, 8cm and 10cm.

Then,

$\mathtt{S = \frac{(6+8+10)cm}{2}=\frac{24cm}{2}=12cm}$

[S stands for Semiperimeter]

$\mathtt{Area\:of \:triangle=\sqrt{s(s-a)(s-b)(s-c)}}$

$\mathtt{=\sqrt{12(12-6)(12-8)(12-10)}}$

$\mathtt{=\sqrt{12\times6\times4\times2}}$

$\mathtt{=\sqrt{576}=24cm}$

Hence the area of the triangle = 24cm²