Math CentralQuandaries & Queries


Question from Julie, a student:

Find the dimensions of a rectangle with an area of 400. Width x ft. Length (2x-7)ft.

we have two responses for you

Hi Julie,

The area of a rectangle is the length tomes the width. You have a length of x feet, a width of (2x - 7) feet and an area of 400 square feet. Thus

x × (2x - 7) = 400

Simplify this equation, factor it and solve for x. You will get two values for x but one of them will be negative. The width of a rectangle can't be negative so only the positive value makes sense.



Hi Julie. The area of a rectangle is the width times the length, so

400 = x (2x-7).

Multiply it:

2x2 - 7x = 400

Complete the square:
2( x2 - (7/2)x ) = 400
2( x2 - (7/2)x + (49/16) ) = 400 + 2(49/16)

2 ( x - (7/4) )2 = 3249 / 8

You finish it and find out what x equals.

Stephen La Rocque

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