QuestionCheck if the scale from triangle with sides 1cm, 2cm, 2.5cm to triangle with sides 3cm, 6cm is $1:3$ .

Studdy Solution

STEP 1

Assumptions1. The lengths of the sides of $\triangle ABC$ are1cm,cm, and.5cm. The lengths of two sides of $\triangle DEF$ are3cm and6cm3. We are trying to determine if the scale from $\triangle ABC$ to $\triangle DEF$ could be $13$

STEP 2

The scale factor between two similar figures is the ratio of their corresponding sides. So, if the scale from $\triangle ABC$ to $\triangle DEF$ is $1$ , then each side of $\triangle DEF$ should be three times the length of the corresponding side of $\triangle ABC$ .

STEP 3

We can check this by multiplying each side of $\triangle ABC$ by3 and comparing the results with the lengths of the sides of $\triangle DEF$ .

STEP 4

Multiply the sides of $\triangle ABC$ by3.
$1cm \times3 =3cm$ $2cm \times3 =6cm$ $2.cm \times3 =7.cm$

STEP 5

Now, compare these results with the lengths of the sides of $\triangle DEF$ . We know that two sides of $\triangle DEF$ are3cm andcm, which match the first two results. However, we don't know the length of the third side of $\triangle DEF$ .

STEP 6

If the third side of $\triangle DEF$ is.5cm, then the scale from $\triangle ABC$ to $\triangle DEF$ would be $13$ . If the third side of $\triangle DEF$ is not.5cm, then the scale would not be $13$ .

STEP 7

Since we don't know the length of the third side of $\triangle DEF$ , we can't definitively determine whether the scale from $\triangle ABC$ to $\triangle DEF$ is $13$ . We can only say that it's possible if the third side of $\triangle DEF$ is7.5cm.

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QuestionCheck if the scale from triangle with sides 1cm, 2cm, 2.5cm to triangle with sides 3cm, 6cm is $1:3$ .

Studdy Solution

STEP 1

Assumptions1. The lengths of the sides of $\triangle ABC$ are1cm,cm, and.5cm. The lengths of two sides of $\triangle DEF$ are3cm and6cm3. We are trying to determine if the scale from $\triangle ABC$ to $\triangle DEF$ could be $13$

STEP 2

The scale factor between two similar figures is the ratio of their corresponding sides. So, if the scale from $\triangle ABC$ to $\triangle DEF$ is $1$ , then each side of $\triangle DEF$ should be three times the length of the corresponding side of $\triangle ABC$ .

STEP 3

We can check this by multiplying each side of $\triangle ABC$ by3 and comparing the results with the lengths of the sides of $\triangle DEF$ .

STEP 4

Multiply the sides of $\triangle ABC$ by3.
$1cm \times3 =3cm$ $2cm \times3 =6cm$ $2.cm \times3 =7.cm$

STEP 5

Now, compare these results with the lengths of the sides of $\triangle DEF$ . We know that two sides of $\triangle DEF$ are3cm andcm, which match the first two results. However, we don't know the length of the third side of $\triangle DEF$ .

STEP 6

If the third side of $\triangle DEF$ is.5cm, then the scale from $\triangle ABC$ to $\triangle DEF$ would be $13$ . If the third side of $\triangle DEF$ is not.5cm, then the scale would not be $13$ .

STEP 7

Since we don't know the length of the third side of $\triangle DEF$ , we can't definitively determine whether the scale from $\triangle ABC$ to $\triangle DEF$ is $13$ . We can only say that it's possible if the third side of $\triangle DEF$ is7.5cm.

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QuestionCheck if the scale from triangle with sides 1cm, 2cm, 2.5cm to triangle with sides 3cm, 6cm is 1:31:31:3.

Studdy Solution

STEP 1

Assumptions1. The lengths of the sides of △ABC\triangle ABC△ABC are1cm,cm, and.5cm. The lengths of two sides of △DEF\triangle DEF△DEF are3cm and6cm3. We are trying to determine if the scale from △ABC\triangle ABC△ABC to △DEF\triangle DEF△DEF could be 131313

STEP 2

STEP 3

We can check this by multiplying each side of △ABC\triangle ABC△ABC by3 and comparing the results with the lengths of the sides of △DEF\triangle DEF△DEF.

STEP 4

Multiply the sides of △ABC\triangle ABC△ABC by3.1cm×3=3cm1cm \times3 =3cm1cm×3=3cm2cm×3=6cm2cm \times3 =6cm2cm×3=6cm2.cm×3=7.cm2.cm \times3 =7.cm2.cm×3=7.cm

STEP 5

Now, compare these results with the lengths of the sides of △DEF\triangle DEF△DEF. We know that two sides of △DEF\triangle DEF△DEF are3cm andcm, which match the first two results. However, we don't know the length of the third side of △DEF\triangle DEF△DEF.

STEP 6

If the third side of △DEF\triangle DEF△DEF is.5cm, then the scale from △ABC\triangle ABC△ABC to △DEF\triangle DEF△DEF would be 131313. If the third side of △DEF\triangle DEF△DEF is not.5cm, then the scale would not be 131313.

STEP 7

Since we don't know the length of the third side of △DEF\triangle DEF△DEF, we can't definitively determine whether the scale from △ABC\triangle ABC△ABC to △DEF\triangle DEF△DEF is 131313. We can only say that it's possible if the third side of △DEF\triangle DEF△DEF is7.5cm.

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QuestionCheck if the scale from triangle with sides 1cm, 2cm, 2.5cm to triangle with sides 3cm, 6cm is $1:3$ .

Assumptions1. The lengths of the sides of $\triangle ABC$ are1cm,cm, and.5cm. The lengths of two sides of $\triangle DEF$ are3cm and6cm3. We are trying to determine if the scale from $\triangle ABC$ to $\triangle DEF$ could be $13$

We can check this by multiplying each side of $\triangle ABC$ by3 and comparing the results with the lengths of the sides of $\triangle DEF$ .

Multiply the sides of $\triangle ABC$ by3.
$1cm \times3 =3cm$ $2cm \times3 =6cm$ $2.cm \times3 =7.cm$

Now, compare these results with the lengths of the sides of $\triangle DEF$ . We know that two sides of $\triangle DEF$ are3cm andcm, which match the first two results. However, we don't know the length of the third side of $\triangle DEF$ .

If the third side of $\triangle DEF$ is.5cm, then the scale from $\triangle ABC$ to $\triangle DEF$ would be $13$ . If the third side of $\triangle DEF$ is not.5cm, then the scale would not be $13$ .

Since we don't know the length of the third side of $\triangle DEF$ , we can't definitively determine whether the scale from $\triangle ABC$ to $\triangle DEF$ is $13$ . We can only say that it's possible if the third side of $\triangle DEF$ is7.5cm.