In the diagram below of triangle ACD, E is a point on line AD and B is a point on line AC, such that line EB is parallel to line DC. If AE = 3, ED = 6, and DC = 15, find the length of line EB.
Is it 3x = 15
x = 5
Well, this is quite a "lengthy" math problem. Let me try to solve it for you, as long as you promise not to "measure" my comedic skills afterward.
Since line EB is parallel to line DC, we have a little wizardry called the "proportionality of parallel sides." It states that if two sides of a triangle are parallel, then the lengths of corresponding segments on those sides are proportional.
In this case, we have two corresponding segments: AE and ED, and EB and BC. Therefore, we can set up a proportion:
AE/ED = EB/BC
Plugging in the given values AE = 3, ED = 6, and DC = 15, we get:
3/6 = EB/BC
Now, solving for EB, we can multiply both sides of the equation by BC:
(3/6) * BC = EB
Simplifying further,
0.5 * BC = EB
Now, let's find BC. Since EB is parallel to DC, we can use the "proportionality of parallel sides" again:
EB/BC = ED/DC
Plugging in the values EB = 0.5 * BC, ED = 6, and DC = 15,
0.5 * BC/BC = 6/15
Simplifying,
0.5 = 6/15
Solving for BC, we have:
BC = (0.5 * 15)/6
BC = 0.5 * 2.5
BC = 1.25
Finally, plugging this value back into the equation for EB:
EB = 0.5 * BC
EB = 0.5 * 1.25
EB = 0.625
So, the length of line EB is 0.625. Remember, though, that this is just a number and has no "lengthy" implications beyond this math problem.
To find the length of line EB, we can use the concept of similar triangles.
Since line EB is parallel to line DC, we can conclude that triangle AEB is similar to triangle ADC.
Using the properties of similar triangles, we can set up the following proportion:
AE/AD = EB/DC
Substituting the given values, we have:
3/(3+6) = EB/15
Simplifying the left-hand side:
1/3 = EB/15
To find EB, we can cross-multiply:
EB = (1/3) * 15
EB = 5
Therefore, the length of line EB is 5.
To find the length of line EB, we can use the concept of similar triangles.
Since line EB is parallel to line DC, triangle AEB is similar to triangle ADC.
We can set up a proportion using the lengths of the corresponding sides:
AE/AD = EB/DC
Plugging in the given values:
3/9 = EB/15
Cross-multiplying:
(3)(15) = EB(9)
45 = EB(9)
Dividing both sides by 9:
EB = 45/9
EB = 5
Therefore, the length of line EB is 5 units.