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Tanya [424]
3 years ago
15

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.

Mathematics
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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Answer:

The goat would cover <u>9 meters</u> in taking 24 steps.

Step-by-step explanation:

<u><em>There is a mistake in the question so the correct question is below:</em></u>

A horse takes 3 steps to walk the same distance for which a goat takes 4 steps. Suppose 1 step of the horse covers 1/2 of a metre. How many metres would the goat cover in taking 24 steps?

Now, to find the meters goat cover in taking 24 steps.

As 1 step of horse covers =  \frac{1}{2} \ meter.

So, 3 step of horse covers = \frac{1}{2} \times 3 =\frac{3}{2} =1.5\ meters.

<u><em>Thus, 3 steps of horse covers = 1.5 meter</em></u><em>s.</em>

<em>As given, the horse takes 3 steps to walk the same distance for which a goat takes 4 steps.</em>

<u><em>So, the distance covers by goat in 4 steps = 1.5 meters.</em></u>

Now, to get the meters goat cover in taking 24 steps by using unitary method:

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Thus, the distance cover by the goat in 24 steps = \frac{1.5}{4}\times 24

= \frac{36}{3}

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