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| Math Central | Quandaries & Queries |
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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.
Penny
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.
Cheers,
Stephen La Rocque
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