Question

If the base and height of a right triangle are 3cm and 4 cm respectively, then the perimeter of the triangle is
cm

Answer 1

Given, the base of the right triangle = 3 cm, height = 4 cm
Let, the hypotenuse of the triangle is $x.$
Using the pythagorean theorem, we get
$x^2=3^2+4^2$
$\Rightarrow x^2=9+16\Rightarrow x^2=25$
Taking square root both sides, we get
$\Rightarrow \sqrt{x^2}=\sqrt{25}$
$\Rightarrow x=\sqrt{5^2}(\because 5^2=25)$
$\Rightarrow x=\pm 5$
$\Rightarrow x=5(\because \text{A side of a triangle cannot be negative}$
$\therefore x=-5\text{is rejected})$

The perimeter of a triangle can be calculated by adding the length of all the sides.

$\therefore$ The perimeter of the given right triangle
$=3+4+5$
$=12$ cm