Question

In the following figure, ABCD is a rectangle, BC = 24cm. DP = 10cm, CD= 15 cm. AP produced intersects BC produced at Q. Find AQ and CQ.​

Answer 1

Given :  ABCD is a rectangle, BC = 24cm. DP = 10cm, CD= 15 cm. AP produced intersects BC produced at Q

To Find : AQ and CQ

Solution:

CD = 15 cm

DP = 10 cm

=> CP = 15 - 10  = 5 cm

ABCD is rectangle

=> CP || AB

=> ΔQPC ≈ ΔQAB

=> CP/AB  =  QP/AQ = QC/BQ

=> 5/15 =  QP/AQ = QC/BQ

=> QP/AQ = QC/BQ = 1/3

QC/BQ = 1/3

=> QC/(QC + BC)  = 1/3

=> 3QC = QC + BC

=> 2QC = BC

=> 2QC = 24

=>  QC = 12

CQ = 12 cm

AQ² = AB² + BQ²

=> AQ² = 15² + (24 + 12)²

=> AQ² = 39²

=> AQ = 39

AQ = 39  cm

CQ = 12   cm

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Answer 2

Step-by-step explanation:

✰ Question ⤵

In the following figure, ABCD is a rectangle, BC = 24cm. DP = 10cm, CD= 15 cm. AP produced intersects BC produced at Q. Find AQ and CQ.

✰ Required Solution ⤵

• CD =15cm
• DP = 10 cm

CP = 15 - 10

= 5 cm

ABCD is triangle

=> CP || AB

=> ∆ QPC = ∆QAB

=> CP/AB = QP/AQ = QC/BQ

=> 5/15 = QP/AP = QC/BC

=> QP/AQ = QC/BC = 113

Q/C = 1/3

=> QC /(QC + BC) = 1/3

=> 3QC = QC + BC

=> 2QC = BC

=> QC = 12

=> CQ = 12cm

AQ^2 = AB^2 + BQ^2

=> AQ^2 = 15^2 + (24 + 12)^2

=> AQ^2 = 39^2

=> AQ = 39

• CQ = 12cm
• AQ = 39cm

Hope it helpful.. ✌️

@Somya2563