Question

Find the area and permieter of an isocieles right angle triangle each of whose equal sides are 10 cm

Answer 1

Answer :-

Area = 50 cm²

Perimeter = 34.14 cm

Solution :-

Lengtg qual sides of the Isosceles riggt triangle = ( a ) = 10 cm

In isoceles triangle Base = Height = Length of equal sides

Area of the triangle = 1/2 * Base * Height

= 1/2 * 10 * 10

= 100/2

= 50 cm²

Therefore the area of the triangle is 50 cm²

Finding the hypostenuse of the triangle

Let the hypotenuse be h

By Pythagoaras theorem

⇒ h² = a² + a²

⇒ h² = 2a²

⇒ h² = 2( 10 )²

⇒ h = 10√2

⇒ h = 10 * 1.414

⇒ h = 14.14

Perimeter of the triangle = a + a + h

= 10 + 10 + 14.14

= 20 + 14.14 = 34.14 cm

Therefore the perimeter of the triangle is 34.14 cm.

Answer 2

QUESTION

Find the area and perimeter of an isosceles right angled triangle each of whose equal sides are 10 cm.

ANSWER

Given that the two sides other than hypotenuse are of length 10 cm both

so,

by Pythagorean theorem

(hypotenuse ) ^2 = (10) ^2 + (10) ^2

(hypotenuse ) ^2 = 200

hypotenuse = 10√2 cm

So,

PERIMETER

OF TRIANGLE = 10 cm + 10 cm + 10√2 cm

Perimeter of triangle = 20 + 10√2 cm

perimeter of triangle = 10 ( 2 +√2) cm

AREA

OF TRIANGLE = 1/2 × base × height

Area of triangle = 1/2× 10 × 10

Area of triangle = 50 cm^2

HENCE..,

PERIMETER OF ∆ = 10(2+√2) CM

AREA OF ∆ = 50 SQUARE CM.