JEE Main 2022 · 29 Jun · Shift 1 · Mathematics Q14

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MathematicsSingle correct+4 / -1Question 14 of 90

A wire of length 22 m is to be cut into two pieces. One of the pieces is to be made into a square and the other into an equilateral triangle. Then, the length of the side of the equilateral triangle, so that the combined area of the square and the equilateral triangle is minimum, is :

\dfrac{22}{9+4\sqrt3}

\dfrac{66}{9+4\sqrt3}

\dfrac{22}{4+9\sqrt3}

\dfrac{66}{4+9\sqrt3}

Answer and worked solution

Official answer: B

Set-up. Square side $x$ , triangle side $y$ , $4x+3y=22$ ; area $x^2+\frac{\sqrt3}4y^2$ .

Minimum. $-\frac38(22-3y)+\frac{\sqrt3}2y=0$ gives $y=\dfrac{66}{9+4\sqrt3}$ .

(B)

Topics:Maxima and minima

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JEE Main 2022 · 29 Jun · Shift 1, Mathematics question 14