Problem 1 :
Say, whether the statement given below is true.
If x / 4 = y / 16, then x / y = 1 / 4
Problem 2 :
Say, whether the statement given below is true.
If p / 3 = q / 5, then (p + 3) / 3 = (q + 3) / 5
Problem 3 :
In the diagram shown below,
PQ / QS = PR / RT
Find the length of QS.
Problem 4 :
International standard paper sizes are commonly used all over the world. The various sizes all have the same width-to-length ratios. Two sizes of paper are shown below, called A4 and A3. The distance labeled x is the geometric mean of 210 mm and 420 mm. Find the value of x.
Problem 5 :
A scale model of the Titanic is 107.5 inches long and 11.25 inches wide. The Titanic itself was 882.75 feet long. How wide was it?
1. Answer :
Given :
x/4 = y/16
Using Alternendo Property,
x/y = 4/16
Simplify.
x/y = 1/4
Hence, the statement is true.
2. Answer :
Given :
p/3 = q/5
Using Componendo Property,
(p + 3)/3 = (q + 5)/5
Because (p + 3)/3 ≠ (q + 3)/5, the conclusions are equivalent.
Hence, the statement is false.
3. Answer :
Given :
PQ/QS = PR/RT
Substitute.
16/x = (30 - 10)/10
Simplify.
16/x = 20/10
16/x = 2/1
By reciprocal property, we have
x/16 = 1/2
Multiply each side by 16.
16 ⋅ (x/16) = (1/2) ⋅ 16
Simplify.
x = 8
Hence, the length of BD is 8 units.
4. Answer :
Using the given information, write proportion.
210/x = x/420
Using cross product property,
x^{2} = 210 ⋅ 420
Take radical on both sides.
√x^{2} = √(210 ⋅ 420)
Simplify.
x = √(210 ⋅ 210 ⋅ 2)
x = 210√2
The geometric mean of 210 and 420 is 210√2, or about 297.
Hence, the distance labeled x in the diagram is about 297 mm.
5. Answer :
One way to solve this problem is to set up a proportion that compares the measurements of the Titanic to the measurements of the scale model
Problem Solving Strategy :
Multiply each side by 11.25.
11.25 ⋅ (x/11.25) = (882.75/107.5) ⋅ 11.25
Simplify.
x = (882.75 ⋅ 11.25) / 107.5
Using calculator, we have
x ≈ 92.4
Hence, the Titanic was about 92.4 feet wide.
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