SOLUTION: the length of a rectangle is 6cm and the width 3 cm. if both are increased by the same amount the area is increased by 70 cm^2 find the length and width of the larger rectangle?
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Question 567303: the length of a rectangle is 6cm and the width 3 cm. if both are increased by the same amount the area is increased by 70 cm^2 find the length and width of the larger rectangle? Answer by Horlaye(27) (Show Source):
You can put this solution on YOUR website! Let the number increased be represented by x. Area of a rectangle = l * w. Therefore : l = 6 + x, w = 3 + x. Hence ( 6 + x ) ( 3 + x ) = 70, then we will expand.
18 + 6x + 3x + x^2 = 70 then,we
change it to quadratic equation
x^2+9x+18-70=0
x^2+9x-52=0
x^2-4x+13x-52=0
x(x-4)13(x-4)=0
(x+13)(x-4)=0
x+13=0 or x-4=0
x = -13 or x = 4
since the length can't take the negative. Therefore the increased number = 4 and the larger rectangle's length is 10cm and the width is 7cm.
