Question

One leg of a right triangle measures 8 units and the hypotenuse measures 12 units. The perimeter of the triangle is irrational. True False

Answer 1

True.

Explanation:

The length of the other side = sqrt ( 12^2 - 8^2)

= sqrt (144 - 64)

= sqrt ( 80) which is irrational so the perimeter is also irrational.

(The sum of a rational number and an irrational is irrational).

Answer 2

TRUE

Explanation:

Length of other leg
`= \sqrt {12^2 - 8^2} \\</p><p>= \sqrt {144 -64} \\</p><p>= \sqrt {80} \\</p><p>= 4\sqrt {5} \\`

Since,
`\sqrt 5` is an irrational number, hence Perimeter of triangle will also be irrational.

TRUE