Answer:
The length of the perpendicular = 20 meters
The length of the base = 48 meters
Step-by-step explanation:
The hypotenuse of the triangle = 52 meters
Let the Length of the perpendicular is = k meters
So, the length of the base = ( k + 28) m
Now, by PYTHAGORAS THEOREM , in a right angled triangle:
[tex](BASE)^{2} + (PERPENDICULAR)^{2} = (HYPOTENUSE)^{2}[/tex]
⇒ Here, [tex](k)^{2} + (k +28) ^{2} = (52)^{2}[/tex]
Also, by Algebraic Identity:
[tex](a+b) ^{2} = a^{2} + b ^{2} + 2ab\\ \implies (k+28) ^{2} = k^{2} + (28) ^{2} + 2(28)(k)\\[/tex]
So, the equation becomes:
[tex](k)^{2} +k^{2} + (28) ^{2} + 2(28)(k) = (52)^{2}[/tex]
or, [tex]2k^{2} + 784+ 56k = 2704\\\implies k^{2} + 28k - 960 = 0[/tex]
or,[tex]k^{2} + 48k -20 k - 960 = 0[/tex]
Solving the equation:
⇒ (k+48)(k-20) = 0 , or (k+48) = 0 , or (k-20) = 0
or, either k = -48 , or k = 20
As k is the length of the side, so k ≠ - 48, k = 20
Hence, the length of the perpendicular = k = 20 meters
and the length of the base is k + 28 = 48 meters
