SAT math problem (这题我是不会做,
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SAT math problem (这题我是不会做,
a right triangle has perimeter 32 and area 20.what is the length of its hypotenuse?
a right triangle has perimeter 32 and area 20.what is the length of its hypotenuse?
![SAT math problem (这题我是不会做,](/uploads/image/z/15127840-64-0.jpg?t=SAT+math+problem+%EF%BC%88%E8%BF%99%E9%A2%98%E6%88%91%E6%98%AF%E4%B8%8D%E4%BC%9A%E5%81%9A%2C)
题意是:
直角三角形周长32,面积20,求斜边长
设两直角边长分别为a,b,则斜边长为c
则
a+b+c=32.(1)
ab/2=20.(2)
a^2+b^2=c^2...(3)
由(1)知
a+b=32-c
(a+b)^2=a^b+b^2+2ab=(32-c)^2
∴c^2+80=(32-c)^2
c=59/4
斜边长为59/4
直角三角形周长32,面积20,求斜边长
设两直角边长分别为a,b,则斜边长为c
则
a+b+c=32.(1)
ab/2=20.(2)
a^2+b^2=c^2...(3)
由(1)知
a+b=32-c
(a+b)^2=a^b+b^2+2ab=(32-c)^2
∴c^2+80=(32-c)^2
c=59/4
斜边长为59/4