Question

The triangle bounded by the lines y = 0, y = 2x and y = -0.5x + k, with k positive, is equal to 80 square units. Find k.​

Answer 1

Step-by-step explanation:

Taking y=0 as the base of the triangle, then the height is the y value where the other two lines intersect, hence where 2x=−0.5x+k , ie: x=k2.5 , and so y=2x=45k . Meanwhile the length of the base is where the y=−0.5x+k line crosses y=0 , ie: 2k . Hence the area of the triangle being half base times height is equal to:

0.5∗2k∗45k=45k2

Setting this to 80 gives:

k=8054−−−√=10

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Answer 2

Answer:

A(0,0) , B(2k/5 , 4k/5) , C(2k ,0) : points of intersection of the 3 points of intersection of the 3 lines

(1/2) * (4k/5) * (2k) = 80 : area given

k = 10 : solve the above equation for k , k positive is a given condition.