Rectangle a has side lengths of 6\text{ cm}6 cm6, space, c, m and 3.5\text{ cm}3.5 cm3, point, 5, space, c, m. the side lengths of rectangle b are proportional to the side lengths of rectangle a. what could be the side lengths of rectangle b? choose 2 answers: choose 2 answers: (choice a) a 3\text{ cm}3 cm3, space, c, m and 1.75\text{ cm}1.75 cm1, point, 75, space, c, m (choice b) b 5\text{ cm}5 cm5, space, c, m and 2.5\text{ cm}2.5 cm2, point, 5, space, c, m (choice c) c 7\text{ cm}7 cm7, space, c, m and 7\text{ cm}7 cm7, space, c, m (choice d) d 12\text{ cm}12 cm12, space, c, m and 5\text{ cm}5 cm5, space, c, m (choice e) e 5.25\text{ cm}5.25 cm5, point, 25, space, c, m and 9\text{ cm}9 cm9, space, c, m

Explanation:

Gotta work on writing the problem, kida hard to read with the coding text.  Anyway, a rectangle with one side  of 6 cm and another  at 3.5 cm, then rectangle B is proportional to that.  Which basically means rectangle B will be multiplied or divided by some number.

To make the concept a little simpler imagine it was a square with sides of length 2.  a proportional square twice as big would have lengths of 4 and half as big would have lengths of 1.

In this case we need measurements where one is 6 multiplied or divided by a number x, and then 3.5 has the same action done on it with the same number.  so again, twice as big would be 12 and 7 while half as big would be 3 and 1.75  anyway, let's look at the options.

A) 3 and 1.75

B) 5 and 2.5

C) 7 and 7

D) 12 and 5

E) 5.25 and 9

Just to have ti written, the original rectangle is 6 by 3.5

So A is obvious since I used it as an example, this is a proportional rectangle half the size of A.

The rest are harder to check except C.  7 and 7 make a square, but we know the side lengths have to be different, so C is easy to tell it's not right.

B we have to check.  Since it's not as obvious as A, we have to check with math more carefully.  What do we have to multiply 6 by to get 5?  Also, you always want to make the largest side of each rectangle proportional to each other.  Anyway, 6 times 5/6 is 5, so for B to be right, 3.5 times 5/6 needs to be equal to 2.5.  Does it?  Nope, its 2.9166 repeating.  So B is not right.

I'm not going to go through so much explanation for the others, if you don't get something let me know.  

D we could also know quickly isn't right since I told you the measurements if the rectangle is changed to one with a side length of 12.  We would need the other to be 7, so 12 and 5 isn't right.

E is our last possibility, since we need to pick two, but let's check anyway.  we need to multiply 6 by 7/8 to get 5.25.  3.5 times 7/8 is 3.0625, so not 9.  Good thing we checked here, because only one answer looks to be right.  Are you sure you put the right numbers?  Or did I misinterpret some?  

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