Answer:
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:
[tex](BASE)^{2} + (PERPENDICULAR) ^{2} = (HYPOTENUSE)^{2}[/tex]
⇒ Here, [tex](k)^{2} + ( k+ 98)^2 =( 122)^2[/tex]
Also, by Algebraic Identity: [tex](a+b)^{2} = a^{2} + b ^{2} + 2ab \implies (k+98)^{2} = k^{2} + (98) ^{2} + 2k(98)[/tex]
or, [tex](k)^{2} + k^{2} + (98) ^{2} + 2k(98) =( 122)^2[/tex]
or, [tex]2k^{2} + 9604 + 196k = 14884\\\implies k^{2} + 98k -2640 = 0[/tex]
Solving the equation: [tex]k^{2} +120k - 22k - 2640 = 0 \implies k(k+120)-22(k+120) = 0[/tex]
⇒ (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
