The sides of a right angled triangle are in a | vedclass

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Question

Let sides be $\mathrm{a}-\mathrm{d}, \mathrm{a}, \mathrm{a}+\mathrm{d},(\mathrm{d}>0)$

$\Rightarrow \quad a^2+(a-d)^2=(a+d)^2$

$\Rightarrow \

Vedclass · Accepted Answer

$6$

Vedclass · Answer

Let sides be $\mathrm{a}-\mathrm{d}, \mathrm{a}, \mathrm{a}+\mathrm{d},(\mathrm{d}>0)$

$\Rightarrow \quad a^2+(a-d)^2=(a+d)^2$

$\Rightarrow \quad a=4 d$

$\Rightarrow \quad 	ext { sides are } 3 d, 4 d, 5 d$

$	ext { As area is } 24$

$\Rightarrow \quad \frac{1}{2} 	imes 3 d 	imes 4 d=24$

$\Rightarrow \quad d=2$

$\Rightarrow \quad 	ext { sides are } 6,8,10$

$\Rightarrow \quad 	ext { smallest side is } 6.$

The sides of a right angled triangle are in arithmetic progression. If the triangle has area $24$ , then what is the length of its smallest side ?

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