Answer
Base = $12$ m
Height = $11$ m
Work Step by Step
We know the following;
Area of triangle = $66 m^2$
Base = $(x+1)$
Height = $x$
The formula for the area of a triangle is $\frac{1}{2}\times base \times height$.
We can substitute the values we know into the formula for area to get a quadratic equation.
Area = $\frac{1}{2}\times base \times height$
66 = $\frac{1}{2}\times (x+1) \times x$
66 = $\frac{x^2+x}{2}$ (Multiply both sides by 2)
$132 = x^2+x$ (Subtract 132 from each side to make it equal 0)
$x^{2}+x-132=0$
We now have our quadratic equation, which we can solve by factoring!
$x^{2}+x-132=0$
$x^{2}+12x-11x-132=0$
$x(x+12)-11(x+12)=0$
$(x-11)(x+12)=0$
To find the solutions for $x$, we can make both brackets = 0.
$(x-11)=0$ or $(x+12)=0$
$x=11$ or $x=-12$
$x$ cannot be a negative value in this case, as we are talking about the height of a triangle, which cannot be below 0. So, $x=11$.
We can now find the base and height of the triangle.
Base = $(11+1)$
= $12$ m
Height = $11$ m
