Answer:
2(8w + 1)
Step-by-step explanation:
Look on either side of the plus sign. What ever you see that is common is a common factor. In this case it is also the greatest common factor.
2 appears on both sides of the plus sign.
2(16w/2 + 2/2)
Answer:
20
Step-by-step explanation:
A)
It looks like the [irregular] hexagon has 3 rectangles and 2 triangles within it.
So let's exclude the triangular corners on bottom left and top right for now.
First we have a large rectangle covering most of the upper left of the polygon. 20 ft × 7 ft = 140 sq.ft.
Now we have a rectangle on the bottom right. The width is 11 ft, so take the 7 away from that, 4 ft. × 14 ft. on bottom. 4 ft × 14 ft = 56 sq.ft.
The last small rectangle fits on the right between the 2 other rectangles. It is 24-20 on top/bottom × 7-6 right/left. 4 ft × 1 ft = 4 sq.ft.
Now for the triangles: bottom left is 11-7 × 24-14 = 4 ft × 10 ft. 1/2bh = 1/2×10×4 = 20 sq.ft.
Top right is 24-20 × 11-5 = 4 ft × 6 ft. 1/2bh = 1/2×4×6 = 12 sq.ft.
B)
Add them all together for the total area (A):
A = 140 + 56 + 4 + 20 + 12 = 140+60+32
= 232 sq.ft.
Hope that explains it well enough! ;)
Answer:
Step-by-step explanation:
Let the other side of the rectangle be y. The perimeter of the rectangle is expressed as P = 2(x+y)
Given P = 30ft, on substituting P = 30 into the expression;
30 = 2(x+y)
x+y = 15
y = 15-x
Also since the area of the rectangle is xy;
A = xy
Substitute y = 15-x into the area;
A = x(15-x)
A = 15x-x²
The function that models its area A in terms of the length x of one of its sides is A = 15x-x²
The side of length x yields the greatest area when dA/dx = 0
dA/dx = 15-2x
15-2x = 0
-2x = -15
x = -15/-2
x = 7.5 ft
Hence the side length, x that yields the greatest area is 7.5ft.
Since y = 15-x
y = 15-7.5
y = 7.5
Area of the rectangle = 7.5*7.5
Area of the rectangle = 56.25ft²
