Right triangle from axes

A line segment has its ends on the coordinate axes and forms with them a triangle of area equal to 36 square units. The segment passes through the point ( 5,2). What is the slope of the line segment?

Correct answer:

k1 =  -0.0149
k2 =  -10.7051

Step-by-step explanation:

S=36 S=2ab ab=2 36=72 k=5a2b=ab  (2b)a=b (5a) (272/a)a=72/a (5a)  (2a72)a=72(5a)  (2a72)a=72 (5a) 2a2144a+360=0  p=2;q=144;r=360 D=q24pr=144242360=17856 D>0  a1,2=2pq±D=4144±17856=4144±2431 a1,2=36±33.40658617698 a1=69.40658617698 a2=2.5934138230199   Factored form of the equation:  2(a69.40658617698)(a2.5934138230199)=0  b1=72/a1=72/69.40661.0374 b2=72/a2=72/2.593427.7626 k1=a1b1=69.40661.0374=0.0149

Our quadratic equation calculator calculates it.

k2=a2b2=2.593427.7626=10.7051



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