Rectangles ABCD and EFGH are similar figures because angles A, B, C, and D are congruent to angles E, F, G, and H, respectively.
If DA equals 19 units, AB equals 8 units, and HE equals 133 units, what does EF equal?
A. 56 units
B. 122 units
C. 7 units
D. 315.88 units
DA/HE = AB/EF, so
19/133 = 8/EF
EF = 56
122
Since rectangles ABCD and EFGH are similar figures, the corresponding sides are proportional.
Let's solve for EF.
In rectangle ABCD, we have DA = 19 units and AB = 8 units. Therefore, the ratio of corresponding sides in rectangle ABCD is DA/AB = 19/8.
In rectangle EFGH, we have HE = 133 units. Now, we can set up a proportion using the ratio of corresponding sides:
DA/AB = EF/HE
Substituting the known values, we get:
19/8 = EF/133
To solve for EF, we can cross-multiply:
19 * 133 = 8 * EF
25307 = 8EF
Divide both sides by 8:
EF = 25307/8
EF ≈ 315.88 units
Therefore, EF is approximately equal to 315.88 units.
The correct answer is D. 315.88 units.
To find the length of EF, we can use the property of similar triangles. Since rectangles ABCD and EFGH are similar figures, the ratio of corresponding sides will be equal.
In rectangle ABCD, DA is given as 19 units, and AB is given as 8 units. In rectangle EFGH, the corresponding sides are EF and HE respectively.
Using the ratio of corresponding sides, we can set up the following proportion:
EF / HE = AB / DA
Substituting the given values, we have:
EF / 133 units = 8 units / 19 units
To solve for EF, we cross-multiply:
EF * 19 units = 8 units * 133 units.
EF * 19 = 1064.
Finally, divide both sides by 19 to isolate EF:
EF = 1064 / 19 ≈ 56 units.
Therefore, EF is approximately 56 units.
So, the correct answer is A. 56 units.