Answer:
The length and width of the rectangular door is 5ft and 9ft respectively
Explanation:
Given
Dimension: (x + 7) and (x + 3)
Area = 45 ft²
Required:
The length and width of the door.
To the calculate the length and width of the rectangular door, we'll make the following assumption
1. Length, L = x + 7
2. Width, W = x + 3.
Having said this, the area of a rectangle is calculated using the following formula.
Area ,= Length * Width
By Substitution
45 = (x + 7)(x + 3)
Open the bracket
45 = x² + 7x + 3x + 21
45 = x² + 10x + 21
Collect like terms
x² + 10x ,+ 21 - 45 = 0
x² + 10x - 24 = 0
Factorize
x² + 12x - 2x - 24 ,= 0
x(x + 12) - 2(x + 12) = 0
(x - 2)(x + 12) = 0
x - 2 = 0 or x + 12 = 0
x = 2 or x = -12
Recall that
Length = x + 7
When x ,= 2, Length = 2 + 7 = 9
When x = -12, Length = -12 + 7 = -5
Width ,= x + 3
When x =2; Width = 2 + 3 = 5
When x = -12, Width = -12 + 3 = -9
But length and width can't be negative.
Hence the length and width of the rectangular door is 5ft and 9ft respectively
Explanation
To calculate the length and the width of the door; we make use of the formula used to calculate area of a rectangle;
This led to a quadratic equation; after solving this equation, we arrived at 2 answers of x (one negative and one positive).
Since the dimension of the rectangle can't be negative, we assumed that the dimension of the rectangle to be the positive values of x