Two inches is approximately _____. 10 cm 5 cm 500 mm .5 m
2 answers:
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Answer:
Area = 370 m²
Cost to paint = £105
Step-by-step explanation:
Area of the wall of a cinema hall = Area of a trapezoid (1)+ Area of a rectangle (2) + Area of a trapezoid (3)
Area of a trapezoid =
where and
are the parallel sides and h is the distance between these sides.
Area of trapezoid (1) =
= 69 m²
Area of the rectangle (2) = Length × Width
= 12 × 15
= 180 m²
Area of the trapezoid (3) =
= 121 m²
Now area of the wall = 69 + 180 + 121
= 370 m²
One tin covers the area = 25 m²
Number of tins required to paint the wall =
=
= 14.8
Therefore, number of tins to be purchased = 15
Cost to paint the complete wall = 15 × £7
= £105
Answer:
The rectangles that have exactly 100 squares are 1 by 100 4 by 11 and 5 by 8
Step-by-step explanation:
The given parameters are;
A 2 by 3 rectangle contains 8 squares
A 3 by 4 rectangle contains 20 squares
A 4 by 6 rectangle contains 50 squares
We note that the number of squares varies proportionately to the increase in the dimension of the rectangle, that is we have;
2 by 3 rectangle contains 8 squares
3 by 4 rectangle contains 20 squares increase by 12 = 3 × 4
4 by 5 rectangle contains 40 squares increase by 20 = 4 × 5
The number of squares formed can therefore be arranged in a matrix as follows(please see attached matrix);
Column, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11
Row
1
2
3
4
5
6
7
8
9
10
11
It will be observed that after reaching a point where the row and column are equal, (x, x) the rate of increase in the number of squares become constant and equal to x × ((x - 1) × 0.5) + 1) = x × (x + 1)/2
From the matrix, the rectangles that have exactly 100 squares are 1 by 100 4 by 11 and 5 by 8 and there are no more as presented in the attached matrix, the number of squares formed keeps increasing for each column and row added.
