A wire of length 340 mm is to be cut into two parts One of the parts is to be made into a square and the other into a rectangle where sides are in the ratio of 12 What is the length of the side of the square in mm such that the combined area of

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A wire of length 340 mm is to be cut into two parts. One of the parts is to be made into a square and the other into a rectangle where sides are in the ratio of 1:2. What is the length of the side of the square (in mm) such that the combined area of

(A) 30 
(B) 40 
(C) 120 
(D) 180 



By:13priya

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(B) 40 
Let two parts be xx and yy and part xx is used to make square and part yy is used to make rectangle.

x+y=340x+y=340

If xx part is used to make square, means it is the parameter of square and each side of square is x4x4

Similarly, for rectangle 2∗(l+b)=y2∗(l+b)=y and l=2bl=2b

2∗3b=y⇒b=y62∗3b=y⇒b=y6 and l=y3l=y3 (we know y=340−xy=340−x)

Question says the combined area of the square and the rectangle is a MINIMUM

A=(x4)2+340−x6∗340−x3A=(x4)2+340−x6∗340−x3

For combined area to be minimum dAdy=0dAdy=0

⇒2x16−2(340−x)18=0⇒2x16−2(340−x)18=0

⇒x=160⇒x=160

But question asks for MINIMUM length of side of square that is x4=40mm

milan-ransingh

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