Question

Question is down below, match the answer choices with the units.

Answer 1

whichWe define:

• A = original area = 100 sq units,

,

• A' = dilated area.

If we dilate a trapezoid in a scale factor k, the area scales as:

`A\rightarrow A^(\prime)=k^2\cdot A\text{.}`

Using the area A = 100 sq units, we have:

`\begin{gathered} A^(\prime)=k^2\cdot100\text{ sq units,} \\ k^2=\frac{A^(\prime)}{100\text{ sq units}}, \\ k=\sqrt[]{\frac{A^(\prime)}{100\text{ sq units}}}\text{.} \end{gathered}`

This formula gives as the scale factor k for witch we must dilate the trapezoid to have an area A'.

1) For A' = 6400 sq units, we have:

`k=\sqrt[]{\frac{6400\text{ sq units}^{}}{100\text{ sq units}}}=\sqrt[]{64}=8.`

2) For A' = 100 sq units, we have:

`k=\sqrt[]{\frac{100\text{ sq units}^{}}{100\text{ sq units}}}=\sqrt[]{1}=1.`

3) For A' = 25 sq units, we have:

`k=\sqrt[]{\frac{25\text{ sq units}^{}}{100\text{ sq units}}}=\sqrt[]{(1)/(4)}=(1)/(2).`

4) For A' = 900 sq units, we have:

`k=\sqrt[]{\frac{900\text{ sq units}^{}}{100\text{ sq units}}}=\sqrt[]{9}=3.`

Answers

• 8

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• 1

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• 1/2

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• 3