Problema Solution

draw a triangle whose shortest side is X inches, whose longest side is twice the shortest side, and whose last side is 3 inches longer than the shortest side.

Answer provided by our tutors

we are unable to provide drawings but we can give some guidance regarding solving for such a triangle; for example, you could suppose that such a triangle exists that is a right triangle, in which case we could let 'x' represent the shortest side, the longest side [the hypotenuse] is then '2x' and the remaining side is 'x+3' inches


for a right triangle, we have:

c^2 = a^2 + b^2

where 'c' is the hypotenuse, 'a' is one leg and 'b' is the other


we have c=2x, a=x, b=x+3, giving:

(2x)^2 = x^2 + (x+3)^2

solving for 'x' we have x = -3/2


since a negative length is not possible, the triangle you need to draw will not be a right triangle


you would require that the longest side, 2x, be greater than the side that is 3 inches longer than the shortest side, so:

2x > x+3

x > 3

...so we need a triangle whose sides are based on x > 3


a way to solve this would be to choose some value for 'x', say x=4 inches, then cut out strips of paper that match the lengths of the necessary sides (2x=8, x+3=7); arrange the 4, 7 and 8 inch strips of paper in such a way that they form a triangle and trace that triangle out! there are an infinite number of possible triangles you could draw, but x=4 solves for the smallest such triangle