please Help me, I don't know how to do this question.
In the illustration(in the link below) , suppose that DE ∥ BC. Find DE. (Assume BC = 10.)
DE = ?
www.webassign.net/ewenmath10/12-4-001-alt.gif
review properties of similar triangles.
why is ABC ~ ADE?
Now recall that that means
DE/BC = AD/AB
THese are similar triangles.
There sides are in proportion
6/DE = 12/10
Solve for DE : )
thank you guys
To find DE, we can use the concept of similar triangles.
In the given diagram, we can see that the lines DE and BC are parallel. This means that the angles they form with the transversal AC are equal.
Using this information, we can form two similar triangles: △ADC and △BEC.
In triangle △ADC, DE is parallel to BC, so the sides DE and AD are proportional. Similarly, in triangle △BEC, DE is parallel to BC, so the sides DE and BE are also proportional.
Let's denote the length of DE as x.
From the diagram, we are given that BC = 10.
Now, since both triangles △ADC and △BEC are similar, we can set up the following proportion:
AD/AC = BE/BC
Substituting the given values, we have:
x/(x+10) = (x+6)/10
To solve this proportion for x, we can cross-multiply:
10x = (x+6)(x+10)
Expanding the right side:
10x = x^2 + 16x + 60
Rearranging the equation into a quadratic form:
x^2 + 6x - 40 = 0
Now we can solve this quadratic equation either by factoring, using the quadratic formula, or by completing the square.
Factoring the quadratic equation gives:
(x + 10)(x - 4) = 0
Setting each factor equal to zero:
x + 10 = 0 or x - 4 = 0
Solving for x:
x = -10 or x = 4
Since lengths cannot be negative, we discard -10 as a solution. Therefore, DE = 4.