Q:

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

Accepted Solution

A:
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 then13 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 [tex]A=\frac{1}{2}\times b\times h[/tex]Here, h=12 and b=5[tex]A=\frac{1}{2}\times 5\times 12[/tex][tex]A=5\times 6[/tex][tex]A=30[/tex]The area of the right angle triangle is 30 units.30 is not a perfect square as [tex]30=2\times 3\times 5[/tex]There is no square pair formed.