P and Q are points on the sides AB and AC of a ABC such that BP=CQ=x, PA= 6 cm,AQ= - Maths - Circles

Question

P and Q are points on the sides AB and AC of a ABC such that
BP=CQ=x, PA= 6 cm,AQ= 20 cm, BC=25 cm If PAQ and quadrilateral BPQC
have equal areas, then the value of x
Urgent

Lovina Kansal · Accepted Answer

Dear student
<img alt="" src=
"https://s3mn%20mnimgs%20com/img/shared/ck-files/ck_581c3477f03fa%20png">
We know that,ar(APQ)+ar(BPQC)=ar(ABC)Therefore, 2(APQ)=ABC    ∵ar(APQ)=ar(BPQC)Applying the sine formula, this is equivalent to 212×20×6×sinA=12x+20x+6sinA⇒240sinA=x+20x+6sinA⇒240=x2+26x+120⇒x2+26x-120=0⇒x2+30x-4x-120=0⇒xx+30-4x+30=0⇒x+30x-4=0And since x>0 the only solution is x=4
Regards

P and Q are points on the sides AB and AC of a ABC such that BP=CQ=x, PA= 6 cm,AQ= 20 cm, BC=25 cm. If PAQ and quadrilateral BPQC have equal areas, then the value of x Urgent

P and Q are points on the sides AB and AC of a ABC such that BP=CQ=x, PA= 6 cm,AQ= 20 cm, BC=25 cm. If PAQ and quadrilateral BPQC have equal areas, then the value of x
Urgent