Question

If the length of the shorter leg of a right triangle is 5 cm and the length of the hypotenuse is 8 cm, find the length of the longer leg.

Answer 1

Answer:

The length of the longer leg is 6.24 cm.

Step-by-step explanation:

Here, the length of the hypotenuse  = 8 cm

The length of shorten leg ( Base) = 5 cm

Let us assume the length of longer leg (Perpendicular)   = k cm

Now, as the given triangle is a right angled triangle.

So, by the PYTHAGORAS THEOREM:

$( Base)^2 + ( Perpendicular)^2 = ( Hypotenuse)^2\\\implies (5)^2 + (k)^2 = (8)^2\\\implies k^2 = 64 - 25 = 39\\\implies k^2 = 39\\k = \sqrt{(39)} = \pm (6.24)$

Now,as k is the length of the side, so it cannot be negative.

⇒   k  =  6.24 cm

Hence, the length of the longer leg is 6.24 cm.