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$Question 9 2pts /_\ABC∼/_\DEF, and the scale factor is 2:5. What is the area of /_\DEF ? The formula for the area of a triangle is A=(bh)/(2). 37.5 square units 6 square units 15 square units 75 square units Question 10 2pts$

Question $9$ $\newline$ $2 \mathrm{pts}$ $\newline$ $\triangle A B C \sim \triangle D E F$ , and the scale factor is $2: 5$ . What is the area of $\triangle D E F$ ? The formula for the area of a triangle is $A=\frac{b h}{2}$ . $\newline$ $37$ . $5$ square units $\newline$ $6$ square units $\newline$ $15$ square units $\newline$ $75$ square units $\newline$ Question $10$ $\newline$ $2 \mathrm{pts}$

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Math Problems

Algebra 1

Scale drawings: word problems

Full solution

Q. Question

9

\newline

2 \mathrm{pts}

\newline

\triangle A B C \sim \triangle D E F

, and the scale factor is

2: 5

. What is the area of

\triangle D E F

? The formula for the area of a triangle is

A=\frac{b h}{2}

\newline

37

5

square units

\newline

6

square units

\newline

15

square units

\newline

75

square units

\newline

Question

10

\newline

2 \mathrm{pts}

Scale Factor Explanation: Given scale factor for similar triangles $ABC$ and $DEF$ is $2:5$ . This means that every length in triangle $DEF$ is $\frac{5}{2}$ times the corresponding length in triangle $ABC$ .
Area Proportionality: The area of similar triangles is proportional to the square of the scale factor. So, if the scale factor is $2:5$ , the area scale factor is $(\frac{2}{5})^2 = \frac{4}{25}$ .
Area Calculation: The area of triangle $ABC$ is given as $37.5$ square units. To find the area of triangle $DEF$ , we multiply the area of $ABC$ by the area scale factor $(\frac{4}{25})$ .
Final Result: Calculate the area of triangle DEF: $37.5 \times (\frac{4}{25}) = (37.5 \times 4) / 25 = \frac{150}{25} = 6$ square units.