Question

in figure, AB is parallel to DC, angle A = 90°, DC = 7 cm, AB = 17 cm and AC = 25 cm. Calculate BC​

Answer 1

ANSWER:

BC is 26cm long.

Given:

• AB // DC
• ∠A = 90
• DC = 7cm
• AC = 25cm

To Find:

• BC

Solution:

As we know, AB// DC

⟹ ∠A + ∠D = 180° (consecutive interior angles)

⟹ 90° + ∠D = 180°

∠D = 90°

Δ DAC is a right angle triangle.

According to Pythagorean theorem:

⟹ (AC)² = (DA)² + (DC)²

⟹ ( 25cm)² = (DC)² + (7cm)²

⟹ 625cm² = (DC)² + 49cm²

⟹ 625cm² - 49cm² = (DC)²

⟹ 576cm² = (DC)²

⟹ √576cm² = DC

⟹ 24cm = DC

Now let us construct a line CX, which is perpendicular to AB and also parallel to AD( which is might given)

⟹ ∠XCD + ∠ACX = 180° (consecutive interior angles)

⟹ ∠XCD + 90° = 180°

⟹ ∠XCD = 90°

We got AXCD as a rectangle ( opposite sides are parallel and all angles are right angles )

⟹ XC = AD ( opposite sides of a rectangle)

⟹ XC = 24cm

⟹ ∠CXB + ∠CXA = 180° ( linear pair)

⟹ ∠CXB + 90° = 180°

⟹ ∠CXB = 90°

⟹ AX = DC ( opposite sides of rectangle)

⟹ AX = 7cm

⟹ AX + XB = 17cm

⟹ 7cm + XB = 17cm

⟹ XB = 10cm

ΔXBC is a right triangle

So, according to Pythagorean theorem

⟹ (XB)² + (XC)² = (CB)²

⟹ 10² + 24² = (CB)²

⟹ 100 + 576 = (CB)²

⟹ 676 = (CB)²

⟹ √676 = CB

⟹ 26 = CB

Answer 2

IDK the real reason..

she just told me that her friends replaced her here.

so she's done.

I'm her cousin btw

could you please tell me how you know her.