Parallelograms have parallel and congruent opposite sides.
The altitude of the parallelogram is 5 cm
Let:
[tex]h \to[/tex] altitude
[tex]P \to[/tex] perimeter
So, we have:
[tex]P =50cm[/tex]
Let x and y be the sides of the parallelogram; so, we have:
[tex]y = x +1[/tex]
and
[tex]P = 2\times(x + y)[/tex]
This gives:
[tex]2\times(x + y) = 50[/tex]
Divide by 2
[tex]x + y = 25[/tex]
Substitute [tex]y = x +1[/tex]
[tex]x + x + 1 = 25[/tex]
[tex]2x + 1 = 25[/tex]
Subtract 1 from both sides
[tex]2x = 24[/tex]
Divide both sides by 2
[tex]x = 12[/tex]
Recall that: [tex]y = x +1[/tex]
[tex]y = 12 + 1[/tex]
[tex]y = 13[/tex]
See attachment for the illustration of the parallelogram.
From the attached parallelogram, we have:
[tex]y^2 = x^2 + h^2[/tex] ---- Pythagoras theorem
So, we have:
[tex]13^2 = 12^2 + h^2[/tex]
[tex]169 = 144 + h^2[/tex]
Collect like terms
[tex]h^2 = 169 - 144[/tex]
[tex]h^2 = 25[/tex]
Take positive square roots
[tex]h = 5[/tex]
Hence, the altitude of the parallelogram is 5 cm
Read more about parallelograms at:
https://brainly.com/question/9680084
