Answer :
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
