Question

A company wants to make frames as part of a new product that they are launching. This frame is rectangular and cut out from bigger sheet of steel, so as to lower down its weight. The inner dimensions of the steel frame are 6 × 11 cm and width of frame is x cm. The final area of frame is 28 cm^2.

Find the width of the frame.​

Answer 1

a) An expression for area of the steel before cutting is 4x^2 + 34x + 66 .

b) The area after cutting is 4x^2 + 34x i.e, 28 cm^2.

c) The coefficient of x of the expression formed in part (a) is 34.

a) Write an expression for area of the steel before cutting?

Area of steel before cutting:

Area = (11 + 2x) × (6 + 2x)

Area = 66 + 22x + 12x + 4x^2

Area = 4x^2 + 34x + 66

b) What will be the area after cutting?

Area of steel after cutting out the 11 × 6 middle:

Area = 4x^2 + 34x + 66 - 66

Area = 4x^2 + 34x

As given the final area should be 28 cm^2.

c) Write the coefficient of x? of the expression formed in part (a)​

Area = 4x^2 + 34x + 66

The coefficient of x is 34.

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