Question

Show that the area of a right triangle of sides 5, 12 and 13 cannot be a square

Answer 1

Answer and Explanation:

Given : Sides of right triangle 5,12 and 13.

To find : Show that the area of a right triangle of sides 5, 12 and 13 cannot be a square ?

Solution :

If 5,12 and 13 are sides of a right angle triangle then

13 is the hypotenuse as it is largest side.

then we take perpendicular as 12 and base as 5.

The area of the right angle triangle is

$A=\frac{1}{2}\times b\times h$

Here, h=12 and b=5

$A=\frac{1}{2}\times 5\times 12$

$A=5\times 6$

$A=30$

The area of the right angle triangle is 30 units.

30 is not a perfect square as $30=2\times 3\times 5$

There is no square pair formed.