The area of a triangle with base 'b' and height 'h' is given by the formula:
[tex]A = \frac{1}{2} bh[/tex]
It is given that the area of a triangle is [tex]1440 cm^2[/tex].
It is given that the base of the triangle is 5 times the height.
So, [tex]b=5 \times h = 5h[/tex]
We have to determine the height of the triangle.
Since, [tex]A = \frac{1}{2}bh[/tex]
[tex]1440 = \frac{1}{2}(5h)h[/tex]
[tex]1440 = \frac{1}{2}(5h^2)[/tex]
[tex]1440 \times 2 = 5h^2[/tex]
[tex]2880= 5h^2[/tex]
[tex]\frac{2880}{5}= h^2[/tex]
[tex]h^2=576[/tex]
So, [tex]h=\sqrt{576}[/tex]
So, h = 24 cm
Therefore, the height of the triangle is 24 cm.
Option 2 is the correct answer.
