Question

Please give the answer of 2

Answer 1

Question

In △ABC , ∠B = 90°.D is the mid point of AB and DE || BC .If AB = 9cm and AC = 15cm , find the perimeter of DECB.

Answer

The perimeter of DECB = 40.5 cm²

Step-by-step explanation

Given information

In △ABC , ∠B = 90°.D is the mid point of AB and DE || BC .If AB = 9cm and AC = 15cm

Need to Find out

Find the perimeter of DECB

Formula used

• 》Area of trapezium = 1/2 h(b1 + b2)

= 1/2 h(b1 + b2)where ,

• h = height
• b1 = base 1
• b2 = base 2

Solution

We can do this using the Pythagoras theorem of right angle triangle to get BC

• → AC is the Hypotenuse of triangle
• → AB is perpendicular
• → BC is the Base

By using Pythagoras theorem

⇒ Hypotenuse ² = Perpendicular ² + Base

⇒ AC² = BC² + AB²

⇒ 15cm² = BC² + 9cm²

⇒ 15cm² - 9cm² = BC²

⇒ 225 - 81 = BC²

⇒ 144 = BC²

Now taking the square root to both side . we get

⇒ √144 = BC

⇒ 12 = BC

⇒ BC = 12cm

_________________________

Again using Pythagoras theorem to get DE

⇒ DE² = AE² - AD²

⇒ DE² = 7.5cm² - 4.5cm²

⇒DE² = 56.25 - 20.25

⇒ DE² = 36

Square root both side .we get

⇒ DE = √36

⇒ DE = 6 cm

__________________________

As we know formula of Perimeter

⇒ Area of trapezium = 1/2 × height (Base1 + Base2)

putting values we get

⇒ Area of trapezium = 1/2 × 4.5 (6 + 12)

⇒ Area of trapezium = 1/2 × 45×18

⇒ Area of trapezium = 1/2 × 81

⇒ Area of trapezium = 40.5 cm²