Rectangle:
P = 2 (L+W) but length is 2 meters longer than wide
then L = W + 2, So
P = 2 (L + W)
24 = 2(W+2+W)
24 = 2 (2 + 2W)
24 = 4 + 4W
So 4W = 24 -4 =20
W = 20/4= 5, L = 5+2= 7
Double check
24 = 2*(5+7) = 2 *12 = 24
The <span>piece of fabric is </span>26.24cm squared
Explanation: 3 x 2 + 10 x + 3 We can Split the Middle Term of this expression to factorise it. In this technique, if we have to factorise an expression like a x 2 + b x + c , we need to think of 2 numbers such that: N 1 ⋅ N 2 = a ⋅ c = 3 ⋅ 3 = 9 and, N 1 + N 2 = b = 10 After trying out a few numbers we get: N 1 = 9 and N 2 = 1 9 ⋅ 1 = 9 , and 9 + ( 1 ) = 10 3 x 2 + 10 x + 3 = 3 x 2 + 9 x + 1 x + 3 = 3 x ( x + 3 ) + 1 ( x + 3 ) ( 3 x + 1 ) ( x + 3 ) is the factorised form for the expression.
c
, we need to think of 2 numbers such that:
N
1
⋅
N
2
=
a
⋅
c
=
3
⋅
3
=
9
and,
N
1
+
N
2
=
b
=
10
After trying out a few numbers we get:
N
1
=
9
and
N
2
=
1
9
⋅
1
=
9
, and
9
+
(
1
)
=
10
3
x
2
+
10
x
+
3
=
3
x
2
+
9
x
+
1
x
+
3
=
3
x
(
x
+
3
)
+
1
(
x
+
3
)
(
3
x
+
1
)
(
x
+
3
)
is the factorised form for the expression.
Firstly let's find the dimension of this large rectangle:(given)
Area of Rectangle = 660 x 66 =43,560 ft²
And we know that 1 acre = 43,560 ft², then each rectangle has an area of 1 acre & the 20 acres will correspond to 20 x 43560 = 871,200 ft²
We know that the 20 acres form a rectangle. We need to know what is their disposition:
1) We would like to know the layout of the rectangles since we have 4 possibilities FOR THE LAYOUTS
Note that W=66 & L=666 = 43,956 ft²/ unit )
lay out shape could be either:(in ft)
1 W by 20 L (Final shape Linear 66 x 13320 = 879,120) or
2 W by 10 L (Final shape Stacked 132 x 6660 = 879,120) or
4 W by 5 L (Final shape Stacked 264 x 3330 = 879,120) or
2) We would like to know the number of participants so that to allocate equal space as well as the pedestrian lane, if possible, if not we will calculated the reserved space allocated for pedestrian/visitors)
3) Depending on the shape given we will calculate the visitor space & we will deduct it from the total space to distribute the remaining among the exhibitors.
4) (SUGGESTION) Assuming it's linear, we will reserve
20ft x 13320 ft = = 266,400 ft² and the remaining 612,720 ft² for exhibitors
5) Depending on the kind of the exhibition, we will divide the 612,720 ft² accordingly
6) How can we select the space allocated for each exhibitor:
the 617,720 ft² could be written as a product of prime factors:
612720 = 2⁴ x 3² x 5 x 23 x 37
If you chose each space will be185 ft² , then we can accommodate up to 3,312 exhibitors.
Obviously you can choose any multiple of the prime factors to specify the area allocated & to calculate the number of exhibitors accordingly
