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3 years ago

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The length of triangle base is 26. A line, which is parallel to the base divides the triangle into two equal area parts. Find th

e length of the segment between triangle legs.

1 answer:

Yanka [14]3 years ago

7 0

Answer:

Step-by-step explanation:

It is given that the length of triangle base is 26, then let ABC be the triangle and BC be the base of the triangle=26.Let DE be the parallel line to the base that divides triangle ABC into two equal area parts.

Now, Let AD=a, DB=b, DE=c, AE=d and EC=e, then

Since, triangle ABC is similar to triangle ADE, thus using basic proportions, we get

$\frac{AD}{AB}=\frac{DE}{BC}=\frac{AE}{AC}$

$\frac{AD}{AD+DB}=\frac{DE}{BC}=\frac{AE}{AE+EC}$

$\frac{a}{a+b}=\frac{c}{26}=\frac{d}{d+e}$

Taking the first two equalities,we get

$\frac{a}{a+b}=\frac{c}{26}$

$c=\frac{26a}{a+b}$

Thus, the length of the segment between triangle legs is $\frac{26a}{a+b}$

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