A similarity transformation is one or more rigid transformations (reflection, rotation, translation) followed by a dilation. When a figure is transformed by a similarity transformation, an image is created that is similar to the original figure. In other words, two figures are similar if a similarity transformation will carry the first figure to the second figure.
The distance from E to side AD is 25/13.
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What is a distance?</h3>
- The length of the line connecting two places is the distance between them.
- If the two points are on the same horizontal or vertical line, the distance can be calculated by subtracting the non-identical values.
To find what is the distance from E to side AD:
- If you draw a diagram, you'll see that triangle AEB is a right triangle with lengths 5, 12, and 13.
- Let's call F the point where E meets side AD, so the problem is to find the length of EF.
- By Angle-Angle Similarity, triangle AFE is similar to triangle BEA. (the right angles are congruent, and both angle FAE and ABE are complementary to angle BAE)
- Since they're similar, the ratios of their side lengths are the same.
- EF/EA = EA/AB (they're corresponding side lengths of similar triangles).
Substitute them with known lengths:
- EF/5 = 5/13
- EF = 5 × (5/13) = 25/13
Therefore, the distance from E to side AD is 25/13.
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The correct answer is given below:
Square ABCD has side lengths of 13 units. Point E lies in the interior of the square such that AE=5 units and BE=12 units. What is the distance from E to side AD? Express your answer as a mixed number.
Answer:
The ratio of the number of female teachers to the number of male teachers is 18:5.
Step-by-step explanation:
First: Review how to write a ratio:
To write a ratio, take the two quantities, and put them on both sides of a colon (:). So, our two quantities our 18 and 5. But, they need to be in a specific order:
There are 18 female teachers and 5 male teachers at Ashley's school. What is the ratio of the number of female teachers to the number of male teachers?
Since, they mentioned the number of female teachers first, we put the quantity of female teachers first. So we will write 18 first and 5 after. So, the ratio is 18:5.
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Topic: Ratios
Answer:
The second amount is 3.72
Step-by-step explanation:
Given
Required
Find Second
Substitute 9.92 for First
Express as fraction
Multiply both sides by 9.92
