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The width of a rectangle is 6 inches less than twice its length Find the dimension of the rectangle if its area is 108 square inches?
Wiki User
∙ 11y ago
Imagine a rectangle, the width is called 'Y' and the length is 'X'. the area is X * Y (because the area of a rectangle is the width and the length multiplied) we know the area is 108 so: XY = 108 http://wiki.answers.com/Q/The_width_of_a_rectangle_is_6_inches_less_than_twice_its_length_Find_the_dimension_of_the_rectangle_if_its_area_is_108_square_inches so basically : Y = 2X - 6 now do simultaneuos equations Y = 2X - 6 XY = 108 you can substitute Y from the first equation into the second one so X(2X - 6) = 108 (now multiply out the brackets by timesing everything inside the brackets (2X - 6) by everything out side the brackets (X)...) i cant do 2xsquared for some reason 2XX - 6X = 108 (simplofy by dividing the equation by two as it is divisble by two) XX - 3X = 54 move 54 to the other side by taking 54 away from both sides XX - 3X - 54 = 0 factorise (X - 9)(X + 6) = 0 now either X - 9 = 0 or X + 6 = 0 because to get the product of 0 you must mutiply it by 0 try both out X - 9 = 0 OR X + 6 = 0 add 9 to both sides subtract 6 from both sides X = 9 X = -6 so X is either 9 or -6 ---- but as we are talking about lengths, X has to be 9 because lengths can not be negative so X = 9 the equation from the begining Y = 2X - 6 will help as we now know X substitute X Y = 2(9) - 6
= 18 - 6
= 12 X (the length) = 9 Y (the width) = 12 wahey! you know the dimensions!
Let the width be (2x+6) and the length be x:
width*length = area
(2x-6)*x = 108 sq inches
2x2-6x-108 = 0
Solving the above quadratic equation works out as:
x = -6 or x = 9 it must be the latter because dimensions can't be negative.
Therefore: width = 12 inches and length = 9 inches
Check: 12*9 = 108 square inches
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∙ 11y ago
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