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# the length of a rectangle is 3 centimeters less than five times its width. its area is 14 centimeters.

the length of a rectangle is 3 centimeters less than five times its width. its area is 14 centimeters. what are the dimensions of the rectangle?

the length of a rectangle is 3 centimeters less than five times its width. its area is 14 centimeters. what are the dimensions of the rectangle?

Let w = width

then

5w-3 = length

w(5w-3) = 14

5w^2-3w = 14

5w^2-3w-14=0

(5w+7)(w-2) = 0

w = {-7/5, 2}

throw out the negative solution leaving

w = 2 centimeters

length:

5w-3 =5(2)-3 =10-3 = 7 centimeters

To express this as an equation, let L represents length and w=width. The length of a rectangle is 3cm less than 5 times its width. This tells us that 3 will be subtracted from 5w. So,

L= 5w-3. Next the area is 14cm and since the area of a rectangle is length*width, it will be expressed as

14=L*w and since L=5w-3

14= (5w-3)*w

14=5w2-3w

5w2-3w-14=0

(5w+7)(w-2)=0

w= -7/5cm or 2cm but the measurement cannot be negative so we will consider 2 instead.

To find length:

L= 5(2)-3

L=10-3

L=7cm.