Terry is drawing isosceles triangles with side lengths a, b, and c such that a = y − x
b = x + z
c = y − z
Where x, y, and z are positive integers and x + y + z < 10.
Find all the possible triples (a, b, c) that satisfy this.

9514 1404 393

{2, 2, 2}, {2, 3, 3}, {2, 4, 4}, {3, 2, 3}, {3, 3, 2}, {3, 3, 4}, {3, 4, 3}, {4, 2, 4}, {4, 3, 3}, {4, 4, 2}, {5, 2, 5}, {6, 2, 6}

Step-by-step explanation:

The requirement that side lengths be greater than 0 means that ...

  y > x > 0

  y > z > 0

Then possible values for x and z are 1, 2, 3, and possible values for y are 3, 4, 5, 6, 7.

When we list the possibilities, and exclude those that do not give isosceles triangles, we find the values of {a, b, c} can be those listed above.

-3

step-by-step explanation:

a drawing really does here:

so i draw the horizontal line y=2 and the vertical line x=-2 at this intersection i put b (this is where my right angle is going to be).   so point b is at (-2,2).   point a is 5 units long and is also on y=2 so this point has to be (3,2) or (-7,2) -doesn't matter i will go with (3,2).

now we know c is at (-2,y) we don't know the y yet bet we know that c is on x=-2.

we have the area of the triangle is .5bh=12.5

we know the base length is 5 (ab)

we have the height is (2-y) if you look at your

plug in

.5(5)(2-y)=12.5

solve for y to get the y-coordinate for c

2.5(2-y)=12.5

divide both sides by 2.5 giving:

2-y=5

now subtract 2 on both sides

-y=3

y=-3