Which two ratios form a proportion a) 1:2 and 4:2 b) 1:2 and 2:4 c) 2:1 and 2:4 d) 2:1 and 6:3

The ratios in option b and d form a proportion.

Step-by-step explanation:

Option a)

1:2 or 1/2 is already in the simple form

Let us reduce 4:2 or 4/2 to check whether it is equal to 1/2 or not

as 4/2 = 2/1 which is NOT equal to 1/2

Thus, 1:2 and 4:2 are NOT in proportions

Option b)

1:2 or 1/2 is already in the simple form

Let us reduce 2:4 or 2/4 to check whether it is equal to 1/2 or not

as 2/4 = 1/2 which is EQUAL to 1/2

Thus, 1:2 and 2:4 are in proportions

Option c)

2:1 or 2/1 is already in the simple form

Let us reduce 2:4 or 2/4 to check whether it is equal to 2/1 or not

as 2/4 = 1/2 which is NOT equal to 2/1

Thus, 2:1 and 2:4 are NOT in proportions

Option d)

2:1 or 2/1 is already in the simple form

Let us reduce 6:3 or 6/3 to check whether it is equal to 2/1 or not

as 6/3 = 2/1 which is equal to 2/1

Thus, 2:1 and 6:3 are in proportions

Therefore, the ratios in option b and d form a proportion.

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step-by-step explanation:

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we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4