Question

123. The bisectors of angle A and angle B of the triangle ABC
meet at P and PQ, PR are parallel to AC and BC.

The perimeter of triangle PQR is 30 centimeters.
What is the length of AB?​

Answer 1

Step-by-step explanation:

$\sf \large \green{\underline{ Question}}$

• The bisectors of angle A and angle B of the triangle ABC meet at P and PQ, PR are parallel to AC and BC.The perimeter of triangle PQR is 30 centimeters. What is the length of AB?

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

• The bisectors of angle A and angle B of the triangle ABC

• meet at P and PQ,

• PR are parallel to AC and BC.

• The perimeter of triangle PQR is 30 centimeters.

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

• What is the length of AB?

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

$\bf \underline\red{according \: to \: the \: question \: : }$

$\sf \: pq //ca \to \: qpa = cap \\ \sf \: qap \to \: pq \: = qa \\ \sf pq//cb \to \: rpb \: = cbp \\ \sf \: rbp \to \: pr \: = rb \: \: \: \: \: \:$

$\sf \large \pink{\underline{then :- }}$

$\sf \large \orange{\underline{perimeter \: of \: pqr:- }} \\ \\ \sf \to \: pq \: + qr \: + \: rp \: = 30cm \\ \sf \to \: qa \: + qr \: + \: rb \: = ab \: \: \: \: \: \: \:$

$\therefore \sf \underline{ \green{so \: length \: of \: ab \: = 30 \: cm}}$

$\sf \large \dag \purple{\underline{more \: information }}:-$

• $\text{perimeter of the triangle = sum of all sides.}$

• $\text{perimeter of the triangle} \sf \: = \frac{1}{2} \times sin \times r$

Answer 2

Answer:

Step-by-step explanation:

\sf \large \green{\underline{ Question}}

Question

The bisectors of angle A and angle B of the triangle ABC meet at P and PQ, PR are parallel to AC and BC.The perimeter of triangle PQR is 30 centimeters. What is the length of AB?

\sf \large \blue{\underline{Given}}

Given

The bisectors of angle A and angle B of the triangle ABC

meet at P and PQ,

PR are parallel to AC and BC.

The perimeter of triangle PQR is 30 centimeters.

\sf \large \purple{\underline{To \: Find}}

ToFind

What is the length of AB?

\sf \large \orange{\underline{Solution :- }}

Solution:−

\bf \underline\red{according \: to \: the \: question \: : }

accordingtothequestion:

\begin{gathered}\sf \: pq //ca \to \: qpa = cap \\ \sf \: qap \to \: pq \: = qa \\ \sf pq//cb \to \: rpb \: = cbp \\ \sf \: rbp \to \: pr \: = rb \: \: \: \: \: \: \\\end{gathered}

pq//ca→qpa=cap

qap→pq=qa

pq//cb→rpb=cbp

rbp→pr=rb

\sf \large \pink{\underline{then :- }}

then:−

\begin{gathered}\sf \large \orange{\underline{perimeter \: of \: pqr:- }} \\ \\ \sf \to \: pq \: + qr \: + \: rp \: = 30cm \\ \sf \to \: qa \: + qr \: + \: rb \: = ab \: \: \: \: \: \: \:\end{gathered}

perimeterofpqr:−

→pq+qr+rp=30cm

→qa+qr+rb=ab

\therefore \sf \underline{ \green{so \: length \: of \: ab \: = 30 \: cm}}∴

solengthofab=30cm

\sf \large \dag \purple{\underline{more \: information }}:-†

moreinformation

:−

\text{perimeter of the triangle = sum of all sides.}perimeter of the triangle = sum of all sides.

\text{perimeter of the triangle} \sf \: = \frac{1}{2} \times sin \times rperimeter of the triangle=

2

1

×sin×r