Question

In the figure above, ABCD is a parallelogram, Line DE is perpendicular to Line AB, Line BG is perpendicular to Line CD, and EBGD is a square. If BG = 12 CM and BC = 13 CM, then find AB​

Answer 1

Step by step explanation:

☛ square , has same side equal:

• BG = GD = DE = EB = 12 cm

⇒ In ∆DEA,

• DE = 12 cm,

• AD = 13 cm.

✍ so we want to find AE ;

✈ (by using Pythagoras Theorem)

• (AE)² + (DE)² = (AD)²

• (AE)² + (12)² = (13)²

• (AE)² = (13 × 13) - (12 × 12)

• (AE)² = 169 - 144

• (AE)² = 25

• AE = √25

• AE = 5

¤ According to the question :

• AE + EB = AB

• 12 + 5 = AB

• AB = 17 cm

${ \huge\boxed{\bold{\therefore\:\:{AB = 17 cm}}}}$