Answer:
9m by 40m : yes
10m by 36m : yes
12m by 60m : no
15m by 30m : no
18m by 25m : no
Explanation:
Essentially this question is asking us which dimensions of the rectangles would form a park that has the same area as the triangular park.
So the first step is to calculate the area of the triangular park.
The area of a triangle can be calculated using the formula, A = (bh)/2
where b = base length and h = height.
We are given the dimensions of the triangle and it appears that the height of the park is 20m while the base length is 36m
So we have A = (bh)/2
we know that b = 36 and h = 20
So area of triangular park = (36 * 20)/2
36 * 20 = 720
720 / 2 = 360
So the area of the triangular park is 360m²
Now we want to find which dimensions of a rectangle would create a park that has the same area of the triangular park, more specifically an area of 360m²
(Note that area of a rectangle is simply length times width )
The first rectangle dimensions are 40m by 9m. These dimensions would create a park with an area of 40 * 9 = 360m². This is the same as the triangular park so the answer would be yes for this one.
The second rectangle dimensions are 10m by 36m These dimensions would create a park with an area of 36 * 10 = 360m², which is also the same as the area of the triangular park meaning the answer for this one is also yes.
The third rectangle dimensions are 12m by 60m. These dimensions would create a park with an area of 60 * 12 = 720m². this is not the same as the area of the triangular park so the answer is no for this one.
The forth rectangle dimensions are 15m by 30m. These dimensions would create a park with an area of 30 * 15 = 450m², which is also not the same as the area of the triangular park meaning that the answer for this one is no.
Finally, the last rectangle dimensions are 18m by 25m. These dimensions would create a park with an area of 18 * 25 = 450m². These dimensions would also not create a park with the same area as the triangular park therefore the answer to this one is also no.