JEE Main 2022 · 27 Jun · Shift 1 · Mathematics Q7

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MathematicsSingle correct+4 / -1Question 7 of 90

The lengths of the sides of a triangle are $10+x^2$ , $10+x^2$ and $20-2x^2$ . If for $x=k$ , the area of the triangle is maximum, then $3k^2$ is equal to :

Answer and worked solution

Official answer: C

Height. Half the base is $10-x^2$ , so $h^2=(10+x^2)^2-(10-x^2)^2=40x^2$ .

Area. $\Delta=(10-x^2)\sqrt{40}\,x$ ; $\frac d{dx}\left(10x-x^3\right)=0$ gives $x^2=\frac{10}3$ .

So $3k^2=10$ .

(C)

Topics:Maxima and minima Properties of triangles

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JEE Main 2022 · 27 Jun · Shift 1, Mathematics question 7