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.