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3 years ago

In the adjoining figure, area of trangle ABC is

Mathematics

1 answer:

Zepler [3.9K]3 years ago

3 0

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

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

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

substitute the given values

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

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

$PQ=4\ cm$

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Step-by-step explanation:

(i) Let the vertices be A(2,0), B(3,2) and C(5,1). Then,

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Since, BC = CA, so the triangle ABC will be an isosceles triangle.

(iii) Let the vertices be A(-5,2), B(-4,4) and C(-2,2). Then,

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skip this part if its not

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substitute -13/20 for (-2/5 - 1/4)

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