Question

在Rt△ABC中,∠C=90° 做AB（斜边）的高CD 已知AD=4 BC=3 求AC 要初二的勾股定理

Answer 1

设DB 的长为 x .

x/3 = 3/(x+4)

x(x+4) = 9

x² +4x = 9

x² +4x +4 = 13

(x+2)² = 13

x+2 = ±√13

x = √13 - 2,(另一个根为负值,舍去).

AB = 4 +√13 - 2

= √13 +2

4/AC = AC/ (√13 +2)

AC² = 4(√13 +2)

AC = 2√(√13 +2)