Math / Geometry

QuestionPENTAGONS If ABCDE PQRST, find the scale factor of ABCDE to PQRST and the perimeter of each polygon. scale factor $=$ $\square$ perimeter $\mathrm{ABCDE}=$ $\square$ 65 perimeter $\mathrm{PQRST}=$ $\square$ 91

Studdy Solution

STEP 1

What is this asking? We're comparing two similar pentagons, ABCDE and PQRST, to find how much bigger one is than the other (the scale factor) and the distance around each pentagon (the perimeter).
We're given that the perimeter of ABCDE is 65.
We're given that the perimeter of PQRST is 91. Watch out! Make sure you match corresponding sides when calculating the scale factor!

STEP 2

1. Calculate the Scale Factor
2. Calculate Perimeter of ABCDE
3. Calculate Perimeter of PQRST

STEP 3

Alright, let's kick things off!
We know the pentagons are similar, which means their corresponding sides are proportional.
This also means their perimeters are proportional!
So, the ratio of their perimeters gives us the scale factor.
Let's call the scale factor $k$ .

STEP 4

We're given that the perimeter of ABCDE is 65 and the perimeter of PQRST is 91.
So, if we're scaling from ABCDE to PQRST, our scale factor $k$ is the perimeter of PQRST divided by the perimeter of ABCDE.

STEP 5

$k = \frac{\text{Perimeter of PQRST}}{\text{Perimeter of ABCDE}} = \frac{91}{65} = \frac{7 \cdot 13}{5 \cdot 13} = \frac{7}{5} \cdot \frac{13}{13} = \frac{7}{5} \cdot 1 = \frac{7}{5}$ So, our scale factor is $\frac{7}{5}$ .
This means that each side of PQRST is $\frac{7}{5}$ times the length of the corresponding side of ABCDE.

STEP 6

We're already given the perimeter of ABCDE as 65!
Easy peasy!

STEP 7

We're also already given the perimeter of PQRST as 91!
Double easy peasy!

STEP 8

The scale factor of ABCDE to PQRST is $\frac{7}{5}$ .
The perimeter of ABCDE is 65.
The perimeter of PQRST is 91.

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QuestionPENTAGONS If ABCDE PQRST, find the scale factor of ABCDE to PQRST and the perimeter of each polygon. scale factor $=$ $\square$ perimeter $\mathrm{ABCDE}=$ $\square$ 65 perimeter $\mathrm{PQRST}=$ $\square$ 91

Studdy Solution

STEP 1

STEP 2

1. Calculate the Scale Factor
2. Calculate Perimeter of ABCDE
3. Calculate Perimeter of PQRST

STEP 3

Alright, let's kick things off!
We know the pentagons are similar, which means their corresponding sides are proportional.
This also means their perimeters are proportional!
So, the ratio of their perimeters gives us the scale factor.
Let's call the scale factor $k$ .

STEP 4

We're given that the perimeter of ABCDE is 65 and the perimeter of PQRST is 91.
So, if we're scaling from ABCDE to PQRST, our scale factor $k$ is the perimeter of PQRST divided by the perimeter of ABCDE.

STEP 5

STEP 6

We're already given the perimeter of ABCDE as 65!
Easy peasy!

STEP 7

We're also already given the perimeter of PQRST as 91!
Double easy peasy!

STEP 8

The scale factor of ABCDE to PQRST is $\frac{7}{5}$ .
The perimeter of ABCDE is 65.
The perimeter of PQRST is 91.

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QuestionPENTAGONS If ABCDE PQRST, find the scale factor of ABCDE to PQRST and the perimeter of each polygon. scale factor === □\square□ perimeter ABCDE=\mathrm{ABCDE}=ABCDE= □\square□ 65 perimeter PQRST=\mathrm{PQRST}=PQRST= □\square□ 91

Studdy Solution

STEP 1

STEP 2

1. Calculate the Scale Factor2. Calculate Perimeter of ABCDE3. Calculate Perimeter of PQRST

STEP 3

Alright, let's **kick things off**!We know the pentagons are similar, which means their corresponding sides are proportional.This also means their perimeters are proportional!So, the ratio of their perimeters gives us the scale factor.Let's call the **scale factor** kkk.

STEP 4

We're given that the perimeter of ABCDE is 65 and the perimeter of PQRST is 91.So, if we're scaling *from* ABCDE *to* PQRST, our scale factor kkk is the perimeter of PQRST divided by the perimeter of ABCDE.

STEP 5

STEP 6

We're already given the **perimeter of ABCDE** as 65!Easy peasy!

STEP 7

We're also already given the **perimeter of PQRST** as 91!Double easy peasy!

STEP 8

The **scale factor** of ABCDE to PQRST is 75 \frac{7}{5} 57​.The **perimeter of ABCDE** is 65.The **perimeter of PQRST** is 91.

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QuestionPENTAGONS If ABCDE PQRST, find the scale factor of ABCDE to PQRST and the perimeter of each polygon. scale factor $=$ $\square$ perimeter $\mathrm{ABCDE}=$ $\square$ 65 perimeter $\mathrm{PQRST}=$ $\square$ 91

1. Calculate the Scale Factor
2. Calculate Perimeter of ABCDE
3. Calculate Perimeter of PQRST

Alright, let's kick things off!
We know the pentagons are similar, which means their corresponding sides are proportional.
This also means their perimeters are proportional!
So, the ratio of their perimeters gives us the scale factor.
Let's call the scale factor $k$ .

We're given that the perimeter of ABCDE is 65 and the perimeter of PQRST is 91.
So, if we're scaling from ABCDE to PQRST, our scale factor $k$ is the perimeter of PQRST divided by the perimeter of ABCDE.

We're already given the perimeter of ABCDE as 65!
Easy peasy!

We're also already given the perimeter of PQRST as 91!
Double easy peasy!

The scale factor of ABCDE to PQRST is $\frac{7}{5}$ .
The perimeter of ABCDE is 65.
The perimeter of PQRST is 91.