Question

if triangle abc similar to triangle pqr , h1 and h2 r the heights abc and pqr repectively AB:PQ = 4:9 and h2 = 13.5 , then the value of h1 is

Answer 1

Given:

If triangle ABC similar to triangle PQR

h1 and h2 r the heights ABC and PQR repectively

AB:PQ = 4:9

h2 = 13.5

To find:

The value of h1

Solution:

We know that,

If two triangles are similar to each other, then the ratio of any two corresponding altitudes or medians or angle bisectors is equal to the ratio of their any two corresponding sides.

Here we have,

ΔABC ~ Δ PQR and h1 & h2 are the heights of ABC and PQR respectively

So, according to the above theorem, we get

$\frac{AB}{PQ} = \frac{h1}{h2}$

Now, substituting the given values of AB:PQ & h2, we get

$\frac{4}{9} = \frac{h1}{13.5}$

$\implies h1 = \frac{4}{9} \times 13.5$

$\implies h1 =4 \times 1.5$

$\implies \bold{h1 = 6}$

Thus, the value of h1 is 6.

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