Question

Square has side lengths of 13 units. Point lies in the interior of the square such that units and units. What is the distance from to side

Answer 1

The distance from E to side AD is 25/13.

What is a distance?

• 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.