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Mathematics

Assertion (A): An isosceles right triangle has area 8 cm2. The length of its hypotenuse is 4 cm.

Reason (R): Area of an isosceles triangle with sides a, a and b is given by 14b4a2+b2\dfrac{1}{4}b\sqrt{4a^2 + b^2}.

  1. A is true, R is false

  2. A is false, R is true

  3. Both A and R are true

  4. Both A and R are false

Mensuration

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Answer

Let base and height of isosceles right triangle be a cm.

Area of triangle = 12× base× height\dfrac{1}{2} \times \text{ base} \times \text{ height}

⇒ 8 = 12×a×a\dfrac{1}{2} \times a \times a

⇒ 8 = 12×a2\dfrac{1}{2} \times a^2

⇒ a2 = 16

⇒ a = 4 cm.

By pythagoras theorem,

Hypotenuse2 = Base2 + Height2

⇒ Hypotenuse2 = 42 + 42

⇒ Hypotenuse2 = 16 + 16

⇒ Hypotenuse2 = 32

⇒ Hypotenuse = 32\sqrt{32}

⇒ Hypotenuse = 424\sqrt{2} cm.

∴ Assertion (A) is false.

Area of an isosceles triangle with sides a, a and b is given by 14b4a2−b2\dfrac{1}{4}b\sqrt{4a^2 - b^2}.

∴ Reason (R) is false.

Hence, option 4 is the correct option.

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