A carpenter is putting a skylight on a roof. If the roof measures 10x +89 by 7x+7 and the skylight measures x+5 by 3x+3, what is the area of the remaining roof after the skylight is built?
thank you
To find the area of the remaining roof after the skylight is built, we need to subtract the area of the skylight from the area of the roof.
The area of a rectangle is given by multiplying its length by its width.
The length of the roof is 10x + 89 and the width is 7x + 7.
The area of the roof is (10x + 89) * (7x + 7).
The length of the skylight is x + 5 and the width is 3x + 3.
The area of the skylight is (x + 5) * (3x + 3).
To find the area of the remaining roof, we subtract the area of the skylight from the area of the roof:
Area of remaining roof = Area of roof - Area of skylight
= (10x + 89) * (7x + 7) - (x + 5) * (3x + 3)
Now let's simplify:
= (70x^2 + 707x + 623) - (3x^2 + 18x + 15)
= 70x^2 + 707x + 623 - 3x^2 - 18x - 15
= 67x^2 + 689x + 608
So, the area of the remaining roof after the skylight is built is 67x^2 + 689x + 608.
To find the area of the remaining roof after the skylight is built, we need to subtract the area of the skylight from the total area of the roof.
First, let's calculate the area of the roof. The roof measures 10x + 89 by 7x + 7, so the area of the roof is:
Area of roof = (10x + 89) * (7x + 7)
Next, let's calculate the area of the skylight. The skylight measures x + 5 by 3x + 3, so the area of the skylight is:
Area of skylight = (x + 5) * (3x + 3)
Now, to find the area of the remaining roof, we subtract the area of the skylight from the area of the roof:
Area of remaining roof = Area of roof - Area of skylight
Area of remaining roof = (10x + 89) * (7x + 7) - (x + 5) * (3x + 3)
To simplify the equation, we can expand the terms and combine like terms:
Area of remaining roof = (70x^2 + 700x + 623x + 623) - (3x^2 + 3x + 15x + 15)
Area of remaining roof = 70x^2 + 1320x + 623 - 3x^2 - 18x - 15
Finally, we combine the like terms:
Area of remaining roof = (70x^2 - 3x^2) + (1320x - 18x) + (623 - 15)
Area of remaining roof = 67x^2 + 1302x + 608
So, the area of the remaining roof after the skylight is built is given by the expression 67x^2 + 1302x + 608.
outer area = (10x+89)(7x+7)= 70x^2 + 693x + 623
skylight area = (x+5)(3x+3)= 3x^2 + 18x + 15
remaining area = 70x^2+693x+623 - (3x^2+18x+15)
= 67x^2 + 675x + 608