The hypotenuse of right triangle is 122 meters long. the difference between the other two sides is 98 meters. find the missing sides. use exact values.

The length of the Base = 22 meters

Length of the perpendicular is = 120 meters

Step-by-step explanation:

The length of the hypotenuse =  122 m

Let base side of the triangle = k meters

So, the perpendicular  side of the triangle is  =  98 + k

Now, by PYTHAGORAS THEOREM , in a right angled triangle:

⇒ Here,

Also, by Algebraic Identity:

or,  

or,

Solving the equation:

⇒ (k+120)(k-22) = 0  , or (k+120) = 0 , or (k-22) = 0

or, either  k = -120 , or k = 22

As k is the length of the side, so k ≠  - 120

Hence, the length of the base = k = 22 meters

and the length of the perpendicular is k + 98 = 120 meters

step-by-step explanation: