Is it possible to have a quadrilateral with sides of length 10, 5, 1, and 8?
Yes, so long as the largest side is not larger than the sum of the other 3 sides (i.e. 20, 2, 2, 2 wouldn't work).
ABCD is a rectangle. AD = x + 10, BC = 2x + 8 and CD = 5. Solve for BD. (Be sure to show all your work!)
Hi Kaylon,
This is cheating. Do your own FLVS homework. If you don't know how, ask your teacher.
To determine if it's possible to have a quadrilateral with sides of length 10, 5, 1, and 8, we need to check if the given side lengths satisfy the triangle inequality theorem for all three possible combinations of sides.
The triangle inequality theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the remaining side. For example, in a triangle with sides a, b, and c, it must satisfy the inequality a + b > c, a + c > b, and b + c > a.
For a quadrilateral, we can consider three possible triangles:
1. Checking 10, 5, and 1:
10 + 5 > 1, which is true.
2. Checking 10, 1, and 8:
10 + 1 > 8, which is true.
3. Checking 5, 1, and 8:
5 + 1 > 8, which is not true.
Since the triangle inequality is not satisfied for the sides 5, 1, and 8, it is not possible to form a quadrilateral with sides of length 10, 5, 1, and 8.