Question

1. the rectangle on the grid is a scale drawing of a field. the scale factor is 1 centimeter to 5 meters. for a, write the area of the rectangle in square centimeters. for b, write the area of the field in square meters. a. square centimeters b. square meters 19. the scale factor of triangle a to triangle b is 1 to \\( \frac{1}{5} \\). what is the value of x? x =

Explanation:

Step1: Identify the scale factor

The scale factor of Triangle A to Triangle B is \(1:\frac{1}{5}\) (wait, actually, if the scale factor from A to B is such that the ratio of corresponding sides is \(\frac{\text{Side of A}}{\text{Side of B}}=\frac{1}{5}\)? Wait, no, looking at the proportion: \(\frac{4}{x}=\frac{1}{5}\)? Wait, no, maybe the scale factor is 5? Wait, the handwritten note has \(\frac{4}{x}=\frac{1}{5}\)? Wait, no, let's re-examine. The problem says "The scale factor of Triangle A to Triangle B is \(1:\frac{1}{5}\)"? Wait, maybe it's a typo, and the scale factor is 5 (since if A is smaller than B, the scale factor from A to B is 5). Wait, the proportion set up is \(\frac{\text{Triangle A}}{\text{Triangle B}}=\frac{4}{x}=\frac{1}{5}\)? No, that would make x larger, but if A is similar to B, the ratio of corresponding sides should be equal to the scale factor. Wait, the triangle A has a hypotenuse of 4, and triangle B has hypotenuse x. The scale factor from A to B is \(1:\frac{1}{5}\)? Wait, no, maybe the scale factor is 5 (since \(1:\frac{1}{5}\) is equivalent to 5:1, meaning B is 5 times larger than A). So the ratio of A to B is \(1:5\), so \(\frac{4}{x}=\frac{1}{5}\)? Wait, no, \(\frac{\text{Side of A}}{\text{Side of B}}=\frac{1}{5}\) would mean B is 5 times A. So solving for x: cross-multiplying, \(1 \times x = 4 \times 5\), so \(x = 20\). Wait, let's do the proportion correctly. If the scale factor from A to B is \(k\), then \(\text{Side of B} = k \times \text{Side of A}\). If the scale factor is 5 (since \(1:\frac{1}{5}\) is inverse, maybe the scale factor is 5), then \(x = 4 \times 5 = 20\). Alternatively, using the proportion \(\frac{4}{x}=\frac{1}{5}\), solving for x: \(x = 4 \times 5 = 20\).

Step2: Solve for x

Using the proportion \(\frac{4}{x}=\frac{1}{5}\) (assuming the scale factor ratio is \(\frac{\text{Side A}}{\text{Side B}}=\frac{1}{5}\)), cross - multiply: \(1\times x = 4\times5\), so \(x = 20\).

Answer:

\(x = 20\)