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The square ABCD has side length 20 cm. E is the midpoint of BC. What is the length of AE?

User Rick Glos
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Final answer:

The length of AE in a square ABCD with side length 20 cm, where E is the midpoint of BC, can be found using the Pythagorean theorem. After calculating, AE is found to be approximately 22.36 cm.

Step-by-step explanation:

The length of AE in a square ABCD with a side length of 20 cm, where E is the midpoint of BC, can be determined using the Pythagorean theorem. By connecting AE, we form two right-angled triangles, ABE and AEC. Since E is the midpoint of side BC which is 20 cm long, BE measures 10 cm. With AB also being 20 cm, triangle ABE is a right-angled triangle.

To find AE, we apply the Pythagorean theorem (a² + b² = c²) to triangle ABE, where AE is the hypotenuse (c), AB is one side (a), and BE is the other side (b).

  • AE² = AB² + BE²
  • AE² = 20² + 10²
  • AE² = 400 + 100
  • AE² = 500
  • AE = √500
  • AE = 22.36 cm (approx)

Therefore, the length of AE is approximately 22.36 cm.

User Lubin
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