Question

In the accompanying diagram, AABC is similar to
A POR, AC = 6, AB = BC = 12, and PR = 8. what is the perimeter of triangle PQR​

Answer 1

$\large\underline{\sf{Given- }}$

• Δ ABC ~ Δ PQR

• AB = 12

• AC = 6

• BC = 12

• PR = 8

$\large\underline{\sf{To\:Find - }}$

• Perimeter of Δ PQR

$\large\underline{\sf{Solution-}}$

Given that,

$\rm :\longmapsto\:\triangle \: ABC \: \sim \: \triangle \: PQR$

$\bf\implies \:\dfrac{AB}{PQ} = \dfrac{BC}{QR} = \dfrac{AC}{PR} \: \: \: \: \: \: \: \red{ \{ \: CPST \: \}}$

Again given that,

• AC = 6

• AB = 12

• AC = 12

• PR = 8

On substituting all these values in above, we get

$\bf\implies \:\dfrac{12}{PQ} = \dfrac{12}{QR} = \dfrac{6}{8}$

$\sf \longmapsto \:\dfrac{12}{PQ} = \dfrac{6}{8} \: \: \: and \: \: \: \dfrac{12}{QR} = \dfrac{6}{8}$

$\rm :\longmapsto\:PQ = \dfrac{12 \times 8}{6} \: \: \: and \: \: \: QR = \dfrac{12 \times 8}{6}$

$\bf\implies \:PQ = 16 \: \: \: and \: \: \: QR = 16$

Now,

We know that,

Perimeter of a triangle means sum of all the three sides.

Thus,

$\rm :\longmapsto\:Perimeter_{(\triangle PQR)} = PQ + QR + PR$

$\rm :\longmapsto\:Perimeter_{(\triangle PQR)} = 16 + 16 + 8$

$\rm :\longmapsto\:Perimeter_{(\triangle PQR)} = 40 \: units$

Additional minute :-

Basic Proportionality Theorem :-

• It states that, if a line is drawn parallel to a side of a triangle, which intersects the other sides into two distinct points, then the line divides the other sides of the triangle in same proportion.

Pythagoras Theorem :-

• It states that, In right angle triangle, the square of the longest side is equal to sum of the squares of other two sides.

Converse of Pythagoras Theorem :-

• It states that, if the square of the longest side is equals to sum of the squares of other two sides, then angle opposite to longest side is right angle.