Recall the formula for finding the area of a rectangle. Define a variable for the width and set up an equation to find the dimensions

Question

Recall the formula for finding the area of a rectangle. Define a
variable for the width and set up an equation to find the dimensions of a
rectangle that has an area 144 square inches, given that the length is 10
inches longer than its width.

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Margaret 2 weeks 2021-09-12T04:40:43+00:00 2 Answers 0

Answers ( )

    0
    2021-09-12T04:41:43+00:00

    Answer:

    x^2+10x=144  

    Step-by-step explanation:

    Given : The length is 10
    inches longer than its width.

                Area of rectangle is 144 sq.inches

    To Find : Define a  variable for the width and set up an equation to find the dimensions of a  rectangle

    Solution:

    Let the width be x

    Since we are given that The length is 10
    inches longer than its width.

    So, Length of rectangle = x+10

    Area of rectangle = Length \times Width

                                 = x \times (x+10)  

    We are given that Area of rectangle is 144 sq.inches

    So,  x \times (x+10) =144  

    x^2+10x=144  

    x^2+18x-8x-144=0  

    x(x+18)-8(x+18)=0  

    (x+18)(x-8)=0  

    x=-18,8  

    Since width cannot be negative

    So, width of rectangle is 8 inches

    Length of rectangle = x+10 = 8+10 = 18

    Hence an equation to find the dimensions of a  rectangle that has an area 144 square inches is x^2+10x=144  

    0
    2021-09-12T04:42:02+00:00

    w=width,
    w(w+10)=144
    ______
    The formula for a rectangle area is length times width.

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