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Question Number 164437 by SLVR last updated on 17/Jan/22

$$Findthemax.areaof\mathrm{\Delta }le$$ $$witthsidesa,b,csuchas$$ $$0<a⩽1;1⩽b⩽2;2⩽c⩽3is$$ $$a)1b)1/2c)2d)3/2$$

Answered by mahdipoor last updated on 17/Jan/22

$$getaandbareconstad\Rightarrow$$ $$S=\frac{ab}{2}sin\theta \Rightarrow \frac{dS}{d\theta }=0=\frac{ab}{2}cos\theta \Rightarrow \theta ={90}^{°}$$ $$\Rightarrow a,b,c=\sqrt{a^2+b^2}S=\frac{ab}{2}$$ $$fora=1andb=2(andc=\sqrt{5})$$ $$\Rightarrow S_{max}=\frac{1\times 2}{2}=1$$

Commented bySLVR last updated on 17/Jan/22

$$extreemlygreatsir...godbless$$ $$yousir$$

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