The bases of a trapezoid are 10 and 12 and the nonparallel sides are 2 and 3. How far must each of the nonparallel sides be extended to form a triangle?
extend each of the 3 and 3 sides until they meet.
I see similar triangles.
Let the 3 unit side be extended by x units
then x/10 = (x+3)/12
12x = 10x + 30
2x = 30
x = 15
Do the same thing for the other side by letting that extension be y units
( I got y = 10)
But where do the extended sides meet each other?
To find out how far each of the nonparallel sides must be extended to form a triangle, you need to subtract the length of each nonparallel side from the sum of the bases.
First, let's label the bases as A = 10 and B = 12, and the nonparallel sides as C = 2 and D = 3.
To form a triangle, you need to extend sides C and D. To find the length of the extensions, we need to calculate the difference between the sum of the bases (A + B) and each nonparallel side (C and D).
The formula to calculate the extension length is:
Extension length = (A + B) - (C + D)
Substituting the given values:
Extension length = (10 + 12) - (2 + 3)
= 22 - 5
= 17
Therefore, each of the nonparallel sides must be extended by a length of 17 to form a triangle.