Question

ABCD is a parallelogram, BC is produced to Q so that ∠DQC = 90°. AP ⊥ DC. If AP = 2.5 cm, BC = 4 cm and DQ = 5 cm, find the length of AB.

[Hint: Area of || gm = CD × AP = AD × DQ]

Answer 1

Given:

• ABCD is a parallelogram
• BC is produced to Q such that ∠DQC = 90°
• AP ⊥ DC, AP = 2.5 cm
• BC = 4 cm
• DQ = 5 cm

To find: Length of AB.

Step 1: Use the hint: Area of parallelogram ABCD = CD × AP = AD × DQ

Step 2: In parallelogram ABCD,

• AB = DC (opposite sides are equal)
• AD = BC (opposite sides are equal)

Step 3: Substitute the known values:

• CD = AB (the side to be found)
• AP = 2.5 cm
• AD = BC = 4 cm
• DQ = 5 cm

Using the area relation:

CD × AP = AD × DQ
⇒ AB × 2.5 = 4 × 5
⇒ AB × 2.5 = 20
⇒ AB = `20/2.5`
⇒ AB = 8 cm