Question

A right triangle has legs of lengths 9 cm and 12 cm. calculate the length of the hypotenuse?

Answer 1

Let the legs of the triangle be a and b, and the hypotenuse c.

Your first instinct might tell you to use the Pythagorean theorem to go about solving this because $c= \sqrt{a^{2}+b^{2}}$. This works, but it is slow.

The fastest way to solve this is to recognize that the right triangle is a special triangle where the ratio of the sides are 3:4:5. This means that if the legs are 9 and 12, then the hypotenuse is 15 because 3*3 is 9, 3*4 is 12, and 3*5 is 15.

Answer 2

Answer:

Length of hypotenuse is 15 cm

Step-by-step explanation:

If a,b are the legs of right triangle

and hypotenuse is c then according to Pythagorean theorem

$c^2=a^2+b^2$

$c^2 =9^2+12^2$

$c^2=81+144$

   $c^2=225$

taking square root ,we get

c = 15

therefore hypotenuse for given right triangle is 15 cm.