The rectangular has a base that is one longer than its height.The area of the rectangles is 56 square feet



Answer :

anbu40

Answer:

dimensions are 7 , 8

Step-by-step explanation:

Framing algebraic expressions and finding the unknown value:

        In this sum, area of the rectangle is given.

Let the height of the rectangle be 'x' feet.

            base of the rectangle = height + 1

                                                 = (x + 1) ft

Area of rectangle = length * width

      x * (x +1) = 56 square feet.

Use distributive property to open the parenthesis,

    x*x +x*1 = 56

     x² + x -56 = 0

Sum = 1

Product = -56

Factors are: 8 , (-7).  {8*(-7) = -56 & 8 + (-7) = 1}

Rewrite the middle term using the factors.

x² + 8x - 7x - 56 = 0

x(x + 8) - 7(x + 8) =0

(x + 8)(x -7) = 0

x + 8 = 0   ;    x - 7 = 0

      x = -8 ;         x = 7

x = -8 is rejected as dimension of a rectangle cannot be a negative number.

  x = 7

height = 7 ft

base = 8 ft