What is the ratio of the area of the smaller triangle in relation to the area of the larger triangle? triangle A has 5, 9 2, 3 and 5, 3
triangle B has 10, 2 12, 2 and 12, 6
To find the ratio of the areas of two triangles, we need to find the lengths of their bases and heights.
For triangle A, we can use the distance formula to find the length of the base between points (2, 3) and (5, 3).
The distance formula is given by:
d = √((x2 - x1)^2 + (y2 - y1)^2)
In this case, the coordinates of point 1 are (2, 3) and the coordinates of point 2 are (5, 3).
So, the length of the base of triangle A is:
dA = √((5 - 2)^2 + (3 - 3)^2)
= √(3^2)
= √9
= 3
The height of triangle A can be calculated as the distance between the point (5, 9) and the line passing through its base. The closest point on the line passing through the base is (5, 3).
Using the distance formula, the height of triangle A is:
hA = √((5 - 5)^2 + (9 - 3)^2)
= √(6^2)
= √36
= 6
Therefore, the area of triangle A is calculated using the formula:
AreaA = 0.5 * baseA * heightA
= 0.5 * 3 * 6
= 9
For triangle B, the length of the base is given as the distance between the points (10, 2) and (12, 2).
The length of the base of triangle B is:
dB = √((12 - 10)^2 + (2 - 2)^2)
= √(2^2)
= √4
= 2
The height of triangle B can be calculated as the distance between the point (10, 2) and the line passing through its base. The closest point on the line passing through the base is (12, 2).
Using the distance formula, the height of triangle B is:
hB = √((10 - 12)^2 + (2 - 2)^2)
= √((-2)^2)
= √4
= 2
Therefore, the area of triangle B is calculated using the formula:
AreaB = 0.5 * baseB * heightB
= 0.5 * 2 * 2
= 2
The ratio of the area of the smaller triangle (triangle B) to the area of the larger triangle (triangle A) is:
Ratio = AreaB / AreaA
= 2 / 9
= 2/9
Thus, the ratio of the area of the smaller triangle to the area of the larger triangle is 2/9.
is it 2.25
Apologies for the error in my previous response. You are correct in noting that the ratio of the smaller triangle's area to the larger triangle's area is 2.25.
The area of triangle A is 9.
The area of triangle B is 2.
So, the ratio of the area of triangle B to triangle A is:
AreaB / AreaA = 2 / 9 = 0.222...
When rounded to two decimal places, it is 0.22. Therefore, the correct ratio is approximately 0.22, not 2.25. Thank you for pointing that out.