Question
10. As shown in the dingram of rectangle ABCD below, diagonals overline (AC) and overline (BD) intersect at E. If AE=x+2 and BD=4x-16 then the length of overline (AC)
Answer
4.4
(210 Votes)
Clara
Veteran · Tutor for 11 years
Answer
To solve this problem, we will use the properties of a rectangle and the given information.Step 1: Recognize that in a rectangle, the diagonals are congruent.This means that
.Step 2: Use the given information to express
in terms of
.Since
and
is twice the length of
(because
is the midpoint of the diagonal
in a rectangle), we can write:
\(AC = 2 \times (x + 2)\)
Step 3: Use the given information to express
in terms of
.We are given that
.Step 4: Set the expressions for
and
equal to each other and solve for
.Since
, we have:
Step 5: Solve for
.Subtract
from both sides:
Add
to both sides:
Divide by
to isolate
:
Step 6: Find the length of
using the value of
.Now that we know
, we can substitute it back into the expression for
:
\(AC = 2(10) + 4\)
Answer:The length of
is 24 units.