PART A)find x using the ratio of the sides 12 cm and 16 cm: x/20=12/16. Show your work
PART B) find x using the ratio of the sides 6 cm and 8 cm. Show your work
PART C) Explain why the answers to a and b should be the same
The triangles are
1st one x,12 cm, 6cm,
the 2nd one is 20 cm, 16 cm, 8 cm,
a. x/20 = 12/16. So, here's what you do: 12 * 20 = 240. 240 / 16 = 15. As a way to doublecheck: 15 * 16 = 240 x = 15.
b. x/20 = 6/8. 6 * 20 = 120. 120 / 8 = 15. Here's another double check: 15 * 8 = 120 x = 15.
c. The answers to (a) and (b) should be the same because they are in ratio. Also, you are looking for x in both and it can't change what it's number is.
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PART A) To find the value of x, we can set up a proportion using the ratio of the sides given:
x/20 = 12/16
To solve this proportion, we can cross-multiply:
16x = 12 * 20
Multiply 12 by 20 to get:
16x = 240
Now, we can solve for x by dividing both sides of the equation by 16:
x = 240/16
Simplifying this expression gives us the value of x:
x = 15 cm
Therefore, the value of x is 15 cm.
PART B) Similarly, to find the value of x using the ratio of the sides 6 cm and 8 cm, we set up a proportion:
x/20 = 6/8
Cross-multiplying gives us:
8x = 6 * 20
Multiply 6 by 20:
8x = 120
Divide both sides of the equation by 8 to solve for x:
x = 120/8
Simplifying this expression gives us:
x = 15 cm
Therefore, the value of x is 15 cm.
PART C) The answers to both Part A and Part B are the same, with x equal to 15 cm. This is because both triangles in Part A and Part B are similar triangles.
Two triangles are considered similar if their corresponding angles are equal, and their corresponding sides are proportional. In this case, both triangles have the same angle measures, and the ratios of their corresponding sides are the same. Therefore, the value of x obtained using the ratios of sides will be the same for both triangles.
In other words, the similarity of the triangles guarantees that the ratio of corresponding sides will lead to the same value of x in both cases.