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 . 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

Question

KnowledgeBoat · Accepted Answer

Let base and height of isosceles right triangle be a cm. Area of triangle = ⇒ 8 = ⇒ 8 = ⇒ a2 = 16 ⇒ a = 4 cm. By pythagoras theorem, Hypotenuse2 = Base2 + Height2 ⇒ Hypotenuse2 = 42 + 42 ⇒ Hypotenuse2 = 16 + 16 ⇒ Hypotenuse2 = 32 ⇒ Hypotenuse = ⇒ Hypotenuse = cm. Assertion (A) is false. Area of an isosceles triangle with sides a, a and b is given by . Reason (R) is false. Hence, option 4 is the correct option.

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 . 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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