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1 answer:
The area of triangle B is 10.5 square units.
The area of triangle C is 10 square units.
Step-by-step explanation:
Step 1:
The area of a triangle is half the product of its base length and height.
The base is the lower end of the triangle and its length is called base length.
The length from the base to the highest point on the triangle is the height.
Step 2:
For triangle B, the base extends for a length of 7 units and the height is 3 units.
The area of triangle B
So the area of triangle B is 10.5 square units.
Step 3:
For triangle C, the base extends for a length of 5 units and the height is 4 units.
The area of triangle C
So the area of triangle C is 10 square units.
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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.
