Part 1 out of 2
Marcello is replacing a rectangular sliding glass door with dimensions of (x + 7) and (x + 3) feet. The area
of the glass door is 45 square feet. What are the length and width of the door? Complete the explanation
of how you got your answer.
Please answer quickly!!

The length and width of the rectangular door is 5ft and 9ft respectively

Step-by-step 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

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