Question

find the perimeter of the shaded triangle from the given figure given that angle A =angle D = 90 °​

Answer 1

Step-by-step explanation:

use Pythagoras in triangle that which is unshaded.

therefore BD =5

use Pythagoras in shaded triangle

therefore DC = 12

therefore perimeter = 13+12+5=30 cm

Answer 2

Answer:

30 cm

Step-by-step explanation:

Δ BAD is a right angled triangle with ∠A = 90° and BD is the hypotenuse.

As per Pythagoras Theorem,

BD² = AB² + AD².

⇒ BD² = 4² + 3²

⇒ BD² = 16 + 9

⇒ BD² = 25

⇒ BD = 5 cm

Now, Δ BDC is a right angled triangle with ∠D = 90° and BC is the hypotenuse.

As per Pythagoras Theorem,

BC² = DB² + CD²

13² = 5² + DC²

169 = 25 + DC²

DC² = 169 - 25

DC² = 144

DC = 12 cm

In Δ BDC , Base = BD = 5cm and  Height = DC = 12cm

Perimeter of the ΔBDC = 1/2 * Base * Height

= 1/2 * 5 * 12

= 30 cm

SO, perimeter of the shaded area is 30 cm.