Answer:
The height of the triangle = 4cm
Step-by-step explanation:
Given, area of the triangle = 10 [tex]cm^{2}[/tex]
Let the height of the triangle be h cm
Given, the base b is 3 cm less than twice its height.
b = 2h - 3 ... (1)
By formula, area of the triangle = [tex]\frac{1}{2}[/tex] bh .. (2)
substitute (1)in (2), we get
Area = [tex]\frac{1}{2}[/tex] (2h-3) h
10 = [tex]\frac{1}{2}[/tex] (2h-3) h
20 = [tex]2h^{2} - 3h[/tex]
[tex]2h^{2} - 3h[/tex] - 20 = 0
solving the equation, we get x = 4, -2.5
The height of the triangle = 4cm
