the area of a rectangle is 77m sq ,and the length of the rectangle is 10 m less than three times the width find the dimension of the rectangle

Let W = the width of the rectangle

Then the length L = 3W - 10

LxW = Area

(3W-10)(W) = 77

3W^2 -10W = 77 Now subtract the 77 to make a quadratic equation in standard form

3W^2 - 10W - 77 = 0 Now factor

(3W +11)(W - 7) = 0

3W + 11 = 0

3W = -11

W = -11/3 But width cannot be negative, so we can throw out this answer

W - 7 = 0

W = 7m

L = 3(7) - 10 = 21 - 10 = 11m

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