Answer:
Question 1) x = 3
Question 2) x = 3
Question 3) x = 9/2, y = 6
Question 4) x = 90
Explanation:
Question 1)
x/2 = 6/4
1. We can simplify the fraction 6/4 by dividing both the denominator and the numerator by 2. --> 3/2
2. x/2 = 3/2, and if the denominator is the same, then the numerator should be the same as well for the equation to work. x = 3.
Question 2)
(x+2)/10 = 2/4
1. This time, we make the denominator of both fractions the same. The smallest common multiple of 10 and 4 is 20, so we make the denominator 20 for both fractions. --> 2(x+2)/20 = 5(2)/20
2. Since the denominator is the same, we can look at the numerator only, because if the numerators are the same, then the fraction itself has the same value. 2(x+2) = 5(2) --> 2x+4 = 10 --> 2x = 6 --> x = 3
Question 3)
The question says that the two triangles are similar. That means that the proportions of the sides of the two triangles are the same.
1. Since the length of the bottom is 2 and 3, the proportion of the side lengths of the two triangles is 2:3.
2. 2:3 = 3:x, and here, we do (3 times 3)=(2 times x) --> 9 = 2x --> x = 9/2
3. 2:3 = 4:y, and here, we do (3 times 4)=(2 times y) --> 12 = 2y --> y = 6
Question 4)
Once again, since the question stated that the two figures are similar, the proportions of the side lengths are the same.
1. We know that the side length relationship between the two images is 1:10 because we have two examples. 12:120, and 6:60.
2. 1:10 = 9:x, and here, we do (10 times 9)=(1 times x) --> 90 = x --> x = 90