Question

Area of an isosceles right triangle is 9 sq cm. Find the length of its hypotenuse.​

Answer 1

Answer:

The length of the hypotenuse of the isosceles right triangle is 6 cm.

Step-by-step-explanation:

NOTE: Refer to the attachment for the diagram.

In figure, △ABC is an isosceles right triangle.

m∠ABC = 90°

AB = BC - - ( 1 )

We have given that,

Area of the isosceles right triangle is 9 cm².

We have to find the length of the hypotenuse.

Now, we know that,

Area of triangle = ½ * Base * Height

⇒ A ( △ABC ) = ½ * BC * AB

⇒ A ( △ABC ) = ½ * AB * AB - - [ From ( 1 ) ]

⇒ 9 = ½ * AB² - - [ Given ]

⇒ AB² = 9 * 2

⇒ AB² = 18 cm² - - ( 2 )

Now,

AB = BC - - [ From ( 1 ) ]

⇒ AB² = BC² - - [ Squaring both sides ]

⇒ BC² = 18 cm² - - ( 3 ) [ From ( 2 ) ]

Now, in △ABC, m∠ABC = 90°

∴ ( AC )² = ( AB )² + ( BC )² - - [ Pythagors theorem ]

⇒ AC² = 18 + 18 - - [ From ( 2 ) & ( 3 ) ]

⇒ AC² = 36

⇒ AC = √36

⇒ AC = √( 6 × 6 )

∴ AC = 6 cm

∴ The length of the hypotenuse of the isosceles right triangle is 6 cm.

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Additional Information:

1. Triangle:

A geometric figure formed by binding three segments and having three corners is called a traingle.

2. Types of triangles:

A. Based on angles

B. Based on sides

3. Based on angles:

A. Acute angled triangle ( < 90° )

B. Right angled triangle ( 90° )

C. Obtuse angled triangle ( > 90° )

4. Based on sides:

A. Equilateral triangle

All sides are equal.

B. Isosceles triangle

Two sides are equal

C. Scalene triangle

No side is equal to any other side.

5. Isosceles right triangle:

A right-angled triangle in which both base and height are of equal measures is called as isosceles right triangle.