SOLUTION: the base of a triangle is (2x+3) feet long and the height is (x+3) feet long. If the area of the triangle is 27 square feet, find the base and height of the triangle.

Question 849: the base of a triangle is (2x+3) feet long and the height is (x+3) feet long. If the area of the triangle is 27 square feet, find the base and height of the triangle.
Found 2 solutions by prabhjyot, ritupuneet:
Answer by prabhjyot(165) (Show Source): You can put this solution on YOUR website!
Area of the triangle =1/2 base* height
given base=(2x+3)
height=(x+3)
area=27
putting in the above formulae
27=1/2*(2x+3)*(x+3)
27=1/2*2x^2+6x+9
27*2=2x^2+6x+9
54=2x^2+6x+9
2x^2+6x+9-54=0
2x^2+6x-45=0
finding the value of x

putting the values in the above equation we get x=3.475,-6.74
taking the positive value of x
base=2x+3=2*3.475+3=9.95
height=x+3=3.475+3=6.475
Answer by ritupuneet(1) (Show Source): You can put this solution on YOUR website!
As we know the formula of area of triangle is
Area of triangle = 1/2*base*height ------(1)
base =(2x+3)
height=(x+3)
Area = 27
Put the value in equation (1)
27 = 1/2*(2x+3)(x+3)
27*2 = (2x+3)x+(2x+3)3
54 = 2x^2+3x+6x+9
54 = 2x^2+9x+9
2x^2+9x+9-54 = 0
2x^2+9x-45=0
by factorization we can write the equation
2x^2+(15-6)x-45=0
2x^2+15x-6x-45=0
x(2x+15)-3(2x+15)=0
(2x+15)(x-3)=0
x=0,-15/2
Ignore the negative value
Base =2x+3 = 2*3+3 = 9
Height = x+3 = 3+3 6

so Base is 9 & Height is 6

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