Joanna plans on hanging 3 pictures of different sizes on the wall of her staircase. She thinks it will look best if all 3 rectangular pictures are similar. The two sizes she has already are 25 in. by 35 in.and 35 in. by 49 in. Which of the following is a possible size of the third picture?
A.
5 in. by 6 in.
B.
30 in. by 42 in.
C.
45 in. by 70 in.
D.
50 in. by 63 in.

Question

23-06-2015
Mathematics

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Joanna plans on hanging 3 pictures of different sizes on the wall of her staircase. She thinks it will look best if all 3 rectangular pictures are similar. The two sizes she has already are 25 in. by 35 in.and 35 in. by 49 in. Which of the following is a possible size of the third picture?
A.
5 in. by 6 in.
B.
30 in. by 42 in.
C.
45 in. by 70 in.
D.
50 in. by 63 in.

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RedRicin RedRicin · Answer 1 · 2015-06-23T17:57:00+02:00

In similar figures, the ratio between corresponding sides are the same.

[tex]\frac{25}{35}=\frac{35}{49}[/tex]

Simplify the two to see that they are equal.
The top and bottom of the left fraction are divisible by 5.
The top and bottom of the right fraction are divisible by 7.

[tex]\frac{5}7=\frac{5}7[/tex]

Of course, the dimensions of that third picture would have to be this fraction.
Let's test these answers.

[tex]\frac{5}6\neq\frac{5}7[/tex] ⇒ A is not a solution

[tex]\frac{30}{42}=\frac{5}7[/tex] ⇒ B is the solution
(divide the top and bottom by 6)