Solved on Dec 11, 2023

If triangle ABC and triangle DEF are similar, then the proportion $\frac{6}{4} = \frac{x}{7}$ must be true.

STEP 1

Assumptions
1. Triangle $ABC$ and triangle $DEF$ are similar.
2. Side $AC$ in triangle $ABC$ corresponds to side $DF$ in triangle $DEF$ .
3. Side $AB$ in triangle $ABC$ corresponds to side $DE$ in triangle $DEF$ .
4. The length of side $AC$ is 7 units.
5. The length of side $AB$ is 6 units.
6. The length of side $DE$ is 4 units.
7. The length of side $DF$ is $x$ units.

STEP 2

Since triangles $ABC$ and $DEF$ are similar, their corresponding sides are proportional. This means that the ratio of the lengths of two corresponding sides in one triangle is equal to the ratio of the lengths of the two corresponding sides in the other triangle.

STEP 3

Set up the proportion using the corresponding sides from both triangles:
$\frac{AB}{DE} = \frac{AC}{DF}$

STEP 4

Substitute the known values into the proportion:
$\frac{6}{4} = \frac{7}{x}$

STEP 5

Cross-multiply to solve for $x$ :
$6 \cdot x = 4 \cdot 7$

STEP 6

Perform the multiplication:
$6x = 28$

STEP 7

Divide both sides of the equation by 6 to solve for $x$ :
$x = \frac{28}{6}$

STEP 8

Simplify the fraction:
$x = \frac{14}{3}$

STEP 9

Convert the improper fraction to a mixed number if necessary:
$x = 4\frac{2}{3}$
The correct proportion that must be true, given the information provided, is:
$\frac{6}{4} = \frac{7}{x}$
Therefore, the answer is a) $\frac{6}{4}=\frac{x}{7}$ .

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If triangle ABC and triangle DEF are similar, then the proportion $\frac{6}{4} = \frac{x}{7}$ must be true.

STEP 1

STEP 2

Since triangles $ABC$ and $DEF$ are similar, their corresponding sides are proportional. This means that the ratio of the lengths of two corresponding sides in one triangle is equal to the ratio of the lengths of the two corresponding sides in the other triangle.

STEP 3

Set up the proportion using the corresponding sides from both triangles:
$\frac{AB}{DE} = \frac{AC}{DF}$

STEP 4

Substitute the known values into the proportion:
$\frac{6}{4} = \frac{7}{x}$

STEP 5

Cross-multiply to solve for $x$ :
$6 \cdot x = 4 \cdot 7$

STEP 6

Perform the multiplication:
$6x = 28$

STEP 7

Divide both sides of the equation by 6 to solve for $x$ :
$x = \frac{28}{6}$

STEP 8

Simplify the fraction:
$x = \frac{14}{3}$

STEP 9

Convert the improper fraction to a mixed number if necessary:
$x = 4\frac{2}{3}$
The correct proportion that must be true, given the information provided, is:
$\frac{6}{4} = \frac{7}{x}$
Therefore, the answer is a) $\frac{6}{4}=\frac{x}{7}$ .

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If triangle ABC and triangle DEF are similar, then the proportion 64=x7\frac{6}{4} = \frac{x}{7}46​=7x​ must be true.

STEP 1

STEP 2

Since triangles ABCABCABC and DEFDEFDEF are similar, their corresponding sides are proportional. This means that the ratio of the lengths of two corresponding sides in one triangle is equal to the ratio of the lengths of the two corresponding sides in the other triangle.

STEP 3

Set up the proportion using the corresponding sides from both triangles:ABDE=ACDF\frac{AB}{DE} = \frac{AC}{DF}DEAB​=DFAC​

STEP 4

Substitute the known values into the proportion:64=7x\frac{6}{4} = \frac{7}{x}46​=x7​

STEP 5

Cross-multiply to solve for xxx:6⋅x=4⋅76 \cdot x = 4 \cdot 76⋅x=4⋅7

STEP 6

Perform the multiplication:6x=286x = 286x=28

STEP 7

Divide both sides of the equation by 6 to solve for xxx:x=286x = \frac{28}{6}x=628​

STEP 8

Simplify the fraction:x=143x = \frac{14}{3}x=314​

STEP 9

Convert the improper fraction to a mixed number if necessary:x=423x = 4\frac{2}{3}x=432​The correct proportion that must be true, given the information provided, is:64=7x\frac{6}{4} = \frac{7}{x}46​=x7​Therefore, the answer is a) 64=x7\frac{6}{4}=\frac{x}{7}46​=7x​.

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

If triangle ABC and triangle DEF are similar, then the proportion $\frac{6}{4} = \frac{x}{7}$ must be true.

Since triangles $ABC$ and $DEF$ are similar, their corresponding sides are proportional. This means that the ratio of the lengths of two corresponding sides in one triangle is equal to the ratio of the lengths of the two corresponding sides in the other triangle.

Set up the proportion using the corresponding sides from both triangles:
$\frac{AB}{DE} = \frac{AC}{DF}$

Substitute the known values into the proportion:
$\frac{6}{4} = \frac{7}{x}$

Cross-multiply to solve for $x$ :
$6 \cdot x = 4 \cdot 7$

Perform the multiplication:
$6x = 28$

Divide both sides of the equation by 6 to solve for $x$ :
$x = \frac{28}{6}$

Simplify the fraction:
$x = \frac{14}{3}$

Convert the improper fraction to a mixed number if necessary:
$x = 4\frac{2}{3}$
The correct proportion that must be true, given the information provided, is:
$\frac{6}{4} = \frac{7}{x}$
Therefore, the answer is a) $\frac{6}{4}=\frac{x}{7}$ .