Question

在Rt△ABC中，∠C=90°，∠A∠B∠C的对边分别是a，b，c，若a+b=14cm，c=10cm，则Rt△ABC的面积是

回答包括过程

Answer 1

a + b = 14
b = 14 - a
c = 10
a² + b² = c²
a² + (14-a)² = 10²
a² + 196 - 28a + a² = 100
2a² - 28a = 100 - 196
a(a-14) = -48
因为：b = 14 - a
所以：a(-b) = -48
三角形面积 = ab/2 = 24 cm²

Answer 2

(a+b)^2=196

a^2+b^2=100

=>a*b=48

S=1/2*a*b
so

S=48/2=24

Answer 3

S = ab/2 = 2ab / 4 = ((a*a + 2ab + b*b ) - (a*a + b*b)) / 4 = ((a+b)*(a+b) - c*c)/4
= (14 * 14 - 10 * 10)/4 = 24 * 4 /4 = 24