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enter image description here

I can easily find the base of the smaller triangle. but wjhat else need to do to determine the value of k?

mathphy
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2 Answers2

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Hint: The triangles are similar.

njguliyev
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  • can you write how? – mathphy Sep 03 '13 at 21:21
  • Their respective angles are equal. – njguliyev Sep 03 '13 at 21:23
  • The triangles are similar, so that means the ratio of the first triangle $?:12:13$ is the same as the ratio of the second $?:?:k$. They are right triangles, and you have already arrived at the length of the base, what other info do you need? – abiessu Sep 03 '13 at 21:23
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    @mathphy Suppose $\theta$ is the angle between the sides of length $12$ and $13$. Then the angle between the side of length $13$ and the base must be $90^\circ-\theta$. Now because the hypotenuses are perpendicular to each other, observe that the angle between the side of length $k$ and the base must therefore be: $$ 180^\circ - 90^\circ - (90^\circ - \theta) = \theta $$ – Adriano Sep 03 '13 at 21:25
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the 3rd side of first rt triangle by pythagorus theorem is $$13^2 - 12^2 = 25 = 5^2 $$ so third side that is the base is 5

so base of other right triangle is $12.2 - 5 = 7.2$

enter image description here now by similar triangle property(AAA)

$$\frac{13}{k} = \frac{12}{7.2}$$

now find k

which is $7.8$

Harish Kayarohanam
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