QuestionPentagon ABCDE is similar to Pentagon RYMNT. Find the missing side: $\frac{A B}{B C}=\frac{R Y}{\square}$ . Options: A E, ER, TN, YM.

Studdy Solution

STEP 1

Assumptions1. Pentagon ABCDE is similar to Pentagon RYMNT. . The ratio of the sides AB and BC of Pentagon ABCDE is equal to the ratio of the sides RY and the unknown side of Pentagon RYMNT.
3. The sides AE and ER of Pentagon ABCDE correspond to the sides TN and YM of Pentagon RYMNT.

STEP 2

Since the pentagons are similar, the ratio of corresponding sides in the two pentagons should be equal. Therefore, we can set up the following equation $\frac{AB}{BC} = \frac{RY}{Unknown}$

STEP 3

We also know that the sides AE and ER of Pentagon ABCDE correspond to the sides TN and YM of Pentagon RYMNT. Therefore, the ratio of AE to ER should be equal to the ratio of TN to YM. We can set up the following equation $\frac{AE}{ER} = \frac{TN}{YM}$

STEP 4

Since the unknown side in the first equation corresponds to the side YM in the second equation, we can equate the two equations to solve for the unknown side. $\frac{RY}{Unknown} = \frac{TN}{YM}$

STEP 5

To solve for the unknown side, we can cross-multiply the equation $RY \cdot YM = Unknown \cdot TN$

STEP 6

Finally, we can solve for the unknown side by dividing both sides of the equation by TN $Unknown = \frac{RY \cdot YM}{TN}$ So, the unknown side in the ratio is equal to the product of the lengths of sides RY and YM divided by the length of side TN.

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QuestionPentagon ABCDE is similar to Pentagon RYMNT. Find the missing side: $\frac{A B}{B C}=\frac{R Y}{\square}$ . Options: A E, ER, TN, YM.

Studdy Solution

STEP 1

Assumptions1. Pentagon ABCDE is similar to Pentagon RYMNT. . The ratio of the sides AB and BC of Pentagon ABCDE is equal to the ratio of the sides RY and the unknown side of Pentagon RYMNT.
3. The sides AE and ER of Pentagon ABCDE correspond to the sides TN and YM of Pentagon RYMNT.

STEP 2

Since the pentagons are similar, the ratio of corresponding sides in the two pentagons should be equal. Therefore, we can set up the following equation $\frac{AB}{BC} = \frac{RY}{Unknown}$

STEP 3

We also know that the sides AE and ER of Pentagon ABCDE correspond to the sides TN and YM of Pentagon RYMNT. Therefore, the ratio of AE to ER should be equal to the ratio of TN to YM. We can set up the following equation $\frac{AE}{ER} = \frac{TN}{YM}$

STEP 4

Since the unknown side in the first equation corresponds to the side YM in the second equation, we can equate the two equations to solve for the unknown side. $\frac{RY}{Unknown} = \frac{TN}{YM}$

STEP 5

To solve for the unknown side, we can cross-multiply the equation $RY \cdot YM = Unknown \cdot TN$

STEP 6

Finally, we can solve for the unknown side by dividing both sides of the equation by TN $Unknown = \frac{RY \cdot YM}{TN}$ So, the unknown side in the ratio is equal to the product of the lengths of sides RY and YM divided by the length of side TN.

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QuestionPentagon ABCDE is similar to Pentagon RYMNT. Find the missing side: ABBC=RY□\frac{A B}{B C}=\frac{R Y}{\square}BCAB​=□RY​. Options: A E, ER, TN, YM.

Studdy Solution

STEP 1

Assumptions1. Pentagon ABCDE is similar to Pentagon RYMNT. . The ratio of the sides AB and BC of Pentagon ABCDE is equal to the ratio of the sides RY and the unknown side of Pentagon RYMNT.3. The sides AE and ER of Pentagon ABCDE correspond to the sides TN and YM of Pentagon RYMNT.

STEP 2

Since the pentagons are similar, the ratio of corresponding sides in the two pentagons should be equal. Therefore, we can set up the following equationABBC=RYUnknown\frac{AB}{BC} = \frac{RY}{Unknown}BCAB​=UnknownRY​

STEP 3

We also know that the sides AE and ER of Pentagon ABCDE correspond to the sides TN and YM of Pentagon RYMNT. Therefore, the ratio of AE to ER should be equal to the ratio of TN to YM. We can set up the following equationAEER=TNYM\frac{AE}{ER} = \frac{TN}{YM}ERAE​=YMTN​

STEP 4

Since the unknown side in the first equation corresponds to the side YM in the second equation, we can equate the two equations to solve for the unknown side.RYUnknown=TNYM\frac{RY}{Unknown} = \frac{TN}{YM}UnknownRY​=YMTN​

STEP 5

To solve for the unknown side, we can cross-multiply the equationRY⋅YM=Unknown⋅TNRY \cdot YM = Unknown \cdot TNRY⋅YM=Unknown⋅TN

STEP 6

Finally, we can solve for the unknown side by dividing both sides of the equation by TNUnknown=RY⋅YMTNUnknown = \frac{RY \cdot YM}{TN}Unknown=TNRY⋅YM​So, the unknown side in the ratio is equal to the product of the lengths of sides RY and YM divided by the length of side TN.

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QuestionPentagon ABCDE is similar to Pentagon RYMNT. Find the missing side: $\frac{A B}{B C}=\frac{R Y}{\square}$ . Options: A E, ER, TN, YM.

Assumptions1. Pentagon ABCDE is similar to Pentagon RYMNT. . The ratio of the sides AB and BC of Pentagon ABCDE is equal to the ratio of the sides RY and the unknown side of Pentagon RYMNT.
3. The sides AE and ER of Pentagon ABCDE correspond to the sides TN and YM of Pentagon RYMNT.

Since the pentagons are similar, the ratio of corresponding sides in the two pentagons should be equal. Therefore, we can set up the following equation $\frac{AB}{BC} = \frac{RY}{Unknown}$

We also know that the sides AE and ER of Pentagon ABCDE correspond to the sides TN and YM of Pentagon RYMNT. Therefore, the ratio of AE to ER should be equal to the ratio of TN to YM. We can set up the following equation $\frac{AE}{ER} = \frac{TN}{YM}$

Since the unknown side in the first equation corresponds to the side YM in the second equation, we can equate the two equations to solve for the unknown side. $\frac{RY}{Unknown} = \frac{TN}{YM}$

To solve for the unknown side, we can cross-multiply the equation $RY \cdot YM = Unknown \cdot TN$

Finally, we can solve for the unknown side by dividing both sides of the equation by TN $Unknown = \frac{RY \cdot YM}{TN}$ So, the unknown side in the ratio is equal to the product of the lengths of sides RY and YM divided by the length of side TN.