The base of the triangle is 15 meters.
Here, we are given that the height of a triangle is 5 m longer than the base.
Let the height of the triangle be h
Then, the base of the triangle will be = h - 5
Further, we are given that area of the triangle = 150 meter square
We know that area of a triangle = 1/2 × base × height
⇒ 150 = 1/2 × h × (h-5)
150 × 2 = h(h-5)
300 = [tex]h^{2}[/tex] - 5h
[tex]h^{2}[/tex] - 5h - 300 = 0
Now, we solve the above quadratic equation by splitting the middle term.
[tex]h^{2}[/tex] + 15h - 20h - 300 = 0
h( h + 15) - 20( h + 15) = 0
(h - 20) (h + 15) = 0
Thus, h = 20 or -15
But since height cannot be negative, h = 20
⇒ base = h - 5
= 20 - 5
= 15 meters
Thus, the base of the triangle is 15 meters.
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