The two rectangles above are similar. If b = 21 mm, and c = 22 mm, and d = 33 mm, what is the length of a?
A.
8 mm
B.
17 mm
C.
7 mm
D.
14 mm
In similar rectangles, the ratios of corresponding sides are equal.
So, we set up the proportion a/b = c/d.
Plugging in the given values, we get a/21 = 22/33
To isolate a, we cross-multiply and solve for a:
a = (22*21)/33 = 14 mm
So the answer is D. 14 mm.
To find the length of "a", we can use the concept of similarity between the two rectangles.
In similar rectangles, corresponding sides are proportional.
Let's compare the sides of the two rectangles:
For rectangle 1: a/b = c/d
For rectangle 2: a/21 = 22/33
We can set up an equation and solve for "a":
(a/21) = (22/33)
To solve for "a", we can cross-multiply:
(22 * 21) = (33 * a)
462 = 33a
To isolate "a", we can divide both sides of the equation by 33:
a = 462/33
a = 14
Therefore, the length of "a" is 14 mm.
The answer is D. 14 mm.
To find the length of side "a" in the given problem, we need to use the concept of similarity of rectangles. When two rectangles are similar, their corresponding sides are proportional.
In this case, we know that the lengths of sides b, c, and d are provided, and we need to find the length of side a. Since sides b and c belong to the smaller rectangle, and sides a and d belong to the larger rectangle, we can set up the proportion:
a/b = d/c
Now, substitute the given values:
a/21 = 33/22
To solve this proportion, cross-multiply:
22a = 21 * 33
Divide both sides by 22 to isolate "a":
a = (21 * 33) / 22
a ≈ 31.5 mm
Therefore, the length of side "a" is approximately 31.5 mm.
None of the options given (8 mm, 17 mm, 7 mm, or 14 mm) match the calculated value. It is possible that there is an error in the problem or the options provided.