Question

P and Q are points on the sides AB and AC respectively of a triangle ABC. PQ is parallel to BC
and divides the triangle ABC into 2 parts, equal in area. The ratio of PA:AB =______

Answer 1

Answer:

Area of ∆APQ=∆PBCQ

As it divides the triangle into equal parts

Now we know,PQ||BC it means ∆APQ~∆ABC

So, Area of ∆APQ/ Area of∆ABC=1/2(As,it divides the triangle into 2 equal parts)

(PA)²/(AB)²=1/2

PA/AB=1/√2

Answer is 1/√2

Answer 2

Given : P and Q are points on the sides AB and AC respectively of a triangle ABC.

PQ is parallel to BC and divides the triangle ABC into 2 parts, equal in area.

To Find :  The ratio of PA: AB  

Solution:

PQ || BC

∠P = ∠B   Corresponding angles

∠Q = ∠C Corresponding angles

=> ΔAPQ ~ ΔABC    AA similarity

Ratio of area of similar triangles = ( ratio of corresponding sides)²

Assume area of ΔABC = 2k  sq units

Then Area of ΔAPQ = 2k/2 = k sq units

Area of Δ APQ / Area of ΔABC  =  (PA / AB) ²

=>  k /2k  =  (PA / AB) ²

=> 1/2 =  (PA / AB) ²

=> 1/√2 = PA/AB

=> PA : AB  = 1  : √2

The ratio of PA: AB= ​ 1  : √2

Learn More:

थेल्स प्रमेय(BPT) का कथन लिखकर उसे ...

brainly.in/question/21435493

if a line divides any two sides of a triangle in the same ratio then the ...

brainly.in/question/25977302