Question

ABCD is rectangle. AP AQ divide L DAB into
three equal parts and BP and BQ Divide L CBA into
three equal parts. Find mL PAB
​

Answer 1

Answer:

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Answer 2

Answer:

let AB=CD=L, and AD=BC=B now given QB=2 we have AQ=L−2

if PD=K (let) we have PA=AP=(B−K)

now by given condition we have 3 Triangles of equal areas

A(PAQ)=A(QBC)=A(PCD)

all the three are right triangles where arae =

2

1

product of perpendicular sides

2

1

(L−2)(B−K) =

2

1

(2B) =

2

1

(K)(L)

if we muliply by 2 we get

2B=(K)(L) gives K=

L

2B

substituting K=

L

2B

in equality (L−2)(B−K)=2B

(L−2)(B−

L

2B

)

or multiply L on both sides gives 2L=(L−2)

2

orL

2

−6L+4=0

we solve for L we get L=

2

[−(−6)±

(−6)

2

−4(1)(4)]

=3±

5

so we have two values (3+

5

) and (3−

5

) for L = AB

now length AQ = AB - 2 or we have (3+

5

−2)=1+

5

which is the positive value allowed for length

Hence the length of AQ=

5

+1