Question

In the adjoining figure, area of trangle ABC is

Answer 1

Answer:

$PQ=4\ cm$

Step-by-step explanation:

see the attached figure with the letter D to better understand the problem

we know that

The segment side AD is the height of triangle ABC

so

Triangles PBQ and ABD are similar by AA Similarity Theorem

The area of triangle ABC is equal to

$A=\frac{1}{2}(BC)(AD)$

we have

$A=48\ cm^2\\BC=12\ cm$

substitute

$48=\frac{1}{2}(12)(AD)$

$AD=8\ cm$

Remember that

If two triangles are similar  then the ratio of its corresponding sides is proportional

so

$\frac{BP}{AB}=\frac{PQ}{AD}$

substitute the given values

$\frac{BP}{2BP}=\frac{PQ}{8}$

$\frac{1}{2}=\frac{PQ}{8}$

$PQ=4\ cm$