What is the length of AE if segment CB is 3y+4 and segment AD is 5y-8?
better explain the diagram for this.
To find the length of AE, we need to know the lengths of segments CB and AD. Let's start by identifying the segments mentioned in the question:
Segment CB = 3y + 4
Segment AD = 5y - 8
Now, let's focus on finding the length of AE.
Segment AE forms the diagonal of quadrilateral ABCD. We can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, triangle ABE is a right triangle, with AB as the hypotenuse and segments AE and BE as the other two sides.
Using the Pythagorean theorem, we have:
AB² = AE² + BE²
Now, we need to find the lengths of AB and BE. From the given information, we can identify segments AB and BE:
Segment AB = Segment CB
Segment BE = Segment AD
Therefore, AB = CB = 3y + 4 and BE = AD = 5y - 8.
Substituting these values into the Pythagorean theorem equation, we have:
(3y + 4)² = AE² + (5y - 8)²
Now, we can expand and simplify the equation to solve for AE:
9y² + 24y + 16 = AE² + 25y² - 80y + 64
Combining like terms, we get:
16y² + 104y + 80 = AE²
Finally, we can subtract 16y² + 104y + 80 from both sides and simplify:
AE² = 16y² + 104y + 80 - 16y² - 104y - 80
This simplifies to:
AE² = 0
Therefore, the length of AE is 0.