ABCD is a kite, so start overline, A, C, end overline
AC
is perpendicular to⊥ start overline, D, B, end overline
DB
and D, E, equals, E, BDE=EB. Calculate the length of start overline, A, C, end overline
AC
, to the nearest tenth of a centimeter.
A
Thank you for the information given. To find the length of line AC, we can use the Pythagorean theorem since AC is perpendicular to DB.
Given:
ABCD is a kite
AC is perpendicular to DB
DE = EB
Let's label the lengths:
AC = x (what we want to find)
DE = EB = y
AD = BC = z
Since DE = EB, we can divide the kite into two congruent right triangles: ADE and CBE. In triangle ADE, we have:
AD = z
DE = y
We can use the Pythagorean theorem to solve for the length of AC:
AC² = AD² + DC²
AC² = z² + (2y)²
AC² = z² + 4y²
In triangle CBE, we have:
BC = z
EB = y
Using the Pythagorean theorem:
CB² = BC² + CE²
CB² = z² + y²
Since DC = CB, we have:
4y = z
Substitute 4y for z in the equations above:
AC² = (4y)² + 4y²
AC² = 16y² + 4y²
AC² = 20y²
Now we know that the length of AC is the square root of 20 times the length of DE:
AC = √(20y)
Since DE = EB, we have:
AC = √(20y) = √(20 * y) = √(20) * y = 4.47 * y
Therefore, the length of AC is approximately 4.47 times the length of DE (or EB).