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

Given:-

ABCD is a Parallelogram,

Line DE is perpendicular to Line AB,

Line BG is perpendicular to Line CD,

EBGD is a Square      and,

BG = 12 cm  and  BC = 13 cm.

Solution:-

here, EBGD is a Square

so, BG = DE = EB = 12 cm

And, ABCD is a Parallelogram

Where, AD = BC = 13 cm

Now, In Δ ADE, Right-angled at E

AE² = AD² - DE²             [ Line DE is perpendicular to Line AB ]

AE² = 13² - 12²

AE = √169 - 144

AE = √25

AE = 5 cm

∴ Line AB = ( Line AE + Line EB )

                ⇒ ( 5 cm + 12 cm )

                ⇒ 17 cm

Hence, AB = 17 cm

Some Important Terms:-

• All sides of Square are Equal.

• Opposite sides of Parallelogram are Equal.

• Pythagoras Theorem:-

Hypotenuse² = Perpendicular² + Base²

• All angles of Square are of 90°.

• Opposite angles of Parallelogram are equal.