The trapezoid above has a base of 38 m and a height of 12 m.
Which set of dimensions would produce a similar figure?
A. base = 114 m, height = 36 m
B. base = 38 m, height = 36 m
C. base = 119 m, height = 36 m
D. base = 109 m, height = 36 m
well, the new base:height ratio would have to be the same: 38/12 = 19/6
So, since all the choices have h=36, which is 6*6, we need a base of 6*19 = 114
Looks like A to me.
To determine which set of dimensions would produce a similar figure to the given trapezoid, we need to understand what makes two figures similar.
Two figures are similar if their corresponding sides are proportional and their corresponding angles are congruent.
In this case, the given trapezoid has a base of 38 m and a height of 12 m. To find a similar figure, we need to find a set of dimensions that has a proportional relationship with the given dimensions.
Let's analyze each option:
A. base = 114 m, height = 36 m
To determine if this set of dimensions is similar to the given trapezoid, we can calculate the ratio of the base and height for both figures:
Ratio for the given trapezoid: base/height = 38/12 = 3.17
Ratio for Option A: base/height = 114/36 = 3.17
Since both ratios are equal, Option A is a possible answer.
B. base = 38 m, height = 36 m
Again, let's calculate the ratio of the base and height for both figures:
Ratio for the given trapezoid: base/height = 38/12 = 3.17
Ratio for Option B: base/height = 38/36 = 1.06
The ratios are not equal, so Option B is not a possible answer.
C. base = 119 m, height = 36 m
Calculating the ratios:
Ratio for the given trapezoid: base/height = 38/12 = 3.17
Ratio for Option C: base/height = 119/36 = 3.31
The ratios are not equal, so Option C is not a possible answer.
D. base = 109 m, height = 36 m
Calculating the ratios:
Ratio for the given trapezoid: base/height = 38/12 = 3.17
Ratio for Option D: base/height = 109/36 = 3.03
The ratios are not equal, so Option D is not a possible answer.
Therefore, the correct answer is Option A: base = 114 m, height = 36 m.