Question

if triangle ABC ~ triangle PQR,area of triangle ABC =81cm^2 and area of triangle PQR =144cm^2 and QR =6cm,then find the BC.

Answer 1

Answer:

4.5

Step-by-step explanation:

I hope I solve your question

Answer 2

Given:

Triangle ABC is similar to triangle PQR, QR =6cm, area of triangle ABC =81cm^2 and area of triangle PQR =144cm^2.

To find:

The length of BC.

Solution:

First of all, we need to know that if two triangles ABC and DEF are similar, then the ratio of their areas is equal to the square of the ratio of their corresponding sides. This means

$\frac{ar(ABC)}{ar(DEF)} = \frac{ {(AB)}^{2} }{ {(DE)}^{2} } = \frac{{(BC)}^{2} }{ {(EF)}^{2}} = \frac{{(AC)}^{2} }{ {(DF)}^{2}}$

So, as given in the question, we have,

Triangle ABC is similar to triangle PQR, ar(ABC) =81cm^2, ar(PQR) = 144cm^2.

Also, QR = 6cm.

Now, in triangles ABC and PQR, BC and QR are corresponding sides, so

$\frac{ar(ABC)}{ar(PQR)} = \frac{ {(BC)}^{2} }{ {(QR)}^{2} }$

$\frac{81}{144} = \frac{ {(BC)}^{2} }{ {(6)}^{2} }$

Taking square root on both sides, we have

$\frac{9}{12} = \frac{BC}{6}$

$\frac{9 \times 6}{12} = BC$

$BC = 4.5cm$

Hence, the length of BC is 4.5cm.