Answer:
Base = 11 cm
Height = 13 cm
Step-by-step explanation:
It is given that the height of a triangle is 2 centimetres more than the base.
Let x cm be the base of triangle. So height of the triangle is x+2 cm.
It is given that if the height is increased by 2 centimetres while the base remains the same, the new area becomes 82.5 centimetres square.
New height = (x+2)+2 = x+4 cm
Area of a triangle is
[tex]A=\dfrac{1}{2}\times base\times height[/tex]
[tex]82.5=\dfrac{1}{2}\times x\times (x+4)[/tex]
[tex]165=x^2+4x[/tex]
[tex]x^2+4x-165=0[/tex]
Splitting the middle term, we get
[tex]x^2+15x-11x-165=0[/tex]
[tex]x(x+15)-11(x+15)=0[/tex]
[tex](x+15)(x-11)=0[/tex]
Using zero product property, we get
[tex]x=-15,11[/tex]
Base of a triangle can not be negative, therefore x=11.
Base = 11 cm
Height = 11+2 = 13 cm
Therefore, the base of original triangle is 11 cm and height is 13 cm.
