QuestionDue parallelogrammi $A B C D$ e $A^{\prime} B^{\prime} C^{\prime} D^{\prime}$ sono simili. Se $A B=30 \mathrm{~cm}$ , $B C=20 \mathrm{~cm}$ e $B^{\prime} C=16 \mathrm{~cm}$ , trova il rapporto di similitudine e $A^{\prime} B^{\prime}$ .

Studdy Solution

STEP 1

Assumptions1. We have two parallelograms $ABCD$ and $A'B'C'D'$ . . These parallelograms are similar.
3. The length of side $AB$ is30 cm.
4. The length of side $BC$ is20 cm.
5. The length of side $B'C'$ is16 cm.
6. We need to find the ratio of similarity and the length of side $A'B'$ .

STEP 2

First, we need to find the ratio of similarity. This can be done by dividing the corresponding sides of the two parallelograms.
$Ratio\, of\, similarity = \frac{Length\, of\, side\, BC\, in\, parallelogram\, A'B'C'D'}{Length\, of\, side\, BC\, in\, parallelogram\, ABC}$

STEP 3

Now, plug in the given values for the lengths of side $BC$ in both parallelograms to calculate the ratio of similarity.
$Ratio\, of\, similarity = \frac{16 cm}{20 cm}$

STEP 4

Calculate the ratio of similarity.
$Ratio\, of\, similarity = \frac{16 cm}{20 cm} =0.8$

STEP 5

Now that we have the ratio of similarity, we can find the length of side $A'B'$ in parallelogram $A'B'C'D'$ . This can be done by multiplying the length of side $AB$ in parallelogram $ABCD$ by the ratio of similarity.
$Length\, of\, side\, A'B' = Length\, of\, side\, AB\, in\, parallelogram\, ABC \times Ratio\, of\, similarity$

STEP 6

Plug in the given value for the length of side $AB$ in parallelogram $ABCD$ and the calculated ratio of similarity to find the length of side $A'B'$ .
$Length\, of\, side\, A'B' =30 cm \times0.8$

STEP 7

Calculate the length of side $A'B'$ .
$Length\, of\, side\, A'B' =30 cm \times0. =24 cm$ So, the ratio of similarity is0. and the length of side $A'B'$ is24 cm.

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QuestionDue parallelogrammi $A B C D$ e $A^{\prime} B^{\prime} C^{\prime} D^{\prime}$ sono simili. Se $A B=30 \mathrm{~cm}$ , $B C=20 \mathrm{~cm}$ e $B^{\prime} C=16 \mathrm{~cm}$ , trova il rapporto di similitudine e $A^{\prime} B^{\prime}$ .

Studdy Solution

STEP 1

Assumptions1. We have two parallelograms $ABCD$ and $A'B'C'D'$ . . These parallelograms are similar.
3. The length of side $AB$ is30 cm.
4. The length of side $BC$ is20 cm.
5. The length of side $B'C'$ is16 cm.
6. We need to find the ratio of similarity and the length of side $A'B'$ .

STEP 2

First, we need to find the ratio of similarity. This can be done by dividing the corresponding sides of the two parallelograms.
$Ratio\, of\, similarity = \frac{Length\, of\, side\, BC\, in\, parallelogram\, A'B'C'D'}{Length\, of\, side\, BC\, in\, parallelogram\, ABC}$

STEP 3

Now, plug in the given values for the lengths of side $BC$ in both parallelograms to calculate the ratio of similarity.
$Ratio\, of\, similarity = \frac{16 cm}{20 cm}$

STEP 4

Calculate the ratio of similarity.
$Ratio\, of\, similarity = \frac{16 cm}{20 cm} =0.8$

STEP 5

STEP 6

Plug in the given value for the length of side $AB$ in parallelogram $ABCD$ and the calculated ratio of similarity to find the length of side $A'B'$ .
$Length\, of\, side\, A'B' =30 cm \times0.8$

STEP 7

Calculate the length of side $A'B'$ .
$Length\, of\, side\, A'B' =30 cm \times0. =24 cm$ So, the ratio of similarity is0. and the length of side $A'B'$ is24 cm.

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Studdy Solution

STEP 1

STEP 2

STEP 3

Now, plug in the given values for the lengths of side BCBCBC in both parallelograms to calculate the ratio of similarity.Ratio of similarity=16cm20cmRatio\, of\, similarity = \frac{16 cm}{20 cm}Ratioofsimilarity=20cm16cm​

STEP 4

Calculate the ratio of similarity.Ratio of similarity=16cm20cm=0.8Ratio\, of\, similarity = \frac{16 cm}{20 cm} =0.8Ratioofsimilarity=20cm16cm​=0.8

STEP 5

STEP 6

Plug in the given value for the length of side ABABAB in parallelogram ABCDABCDABCD and the calculated ratio of similarity to find the length of side A′B′A'B'A′B′.Length of side A′B′=30cm×0.8Length\, of\, side\, A'B' =30 cm \times0.8LengthofsideA′B′=30cm×0.8

STEP 7

Calculate the length of side A′B′A'B'A′B′.Length of side A′B′=30cm×0.=24cmLength\, of\, side\, A'B' =30 cm \times0. =24 cmLengthofsideA′B′=30cm×0.=24cmSo, the ratio of similarity is0. and the length of side A′B′A'B'A′B′ is24 cm.

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Now, plug in the given values for the lengths of side $BC$ in both parallelograms to calculate the ratio of similarity.
$Ratio\, of\, similarity = \frac{16 cm}{20 cm}$

Calculate the ratio of similarity.
$Ratio\, of\, similarity = \frac{16 cm}{20 cm} =0.8$

Plug in the given value for the length of side $AB$ in parallelogram $ABCD$ and the calculated ratio of similarity to find the length of side $A'B'$ .
$Length\, of\, side\, A'B' =30 cm \times0.8$

Calculate the length of side $A'B'$ .
$Length\, of\, side\, A'B' =30 cm \times0. =24 cm$ So, the ratio of similarity is0. and the length of side $A'B'$ is24 cm.