Answer
$h=1.84$ $yards$
Work Step by Step
Computing for the area of the triangle:
$A=\frac{bh}{2}$
$10=\frac{(x+5+x+1+3)(2x)}{2}$
$10=\frac{(2x+9)(2x)}{2}$
$20=4x^2+18x$
$10=2x^2+9x$
$2x^2+9x-10=0$
Use the quadratic formula: $x = \frac{-b±\sqrt{b^2-4ac}}{2a}$
$a=2$, $b=9$, $c=-10$
$x = \frac{-9±\sqrt{9^2-(4⋅2⋅-10)}}{2⋅2}$
$x = \frac{-9±\sqrt{81-(-80)}}{4}$
$x = \frac{-9±\sqrt{161}}{4}$
Since measurements cannot be negative, therefore:
$x = \frac{-9+\sqrt{161}}{4}$
$x = 0.92$ $yard$
Thus, the height is:
$h=2x=2(0.92)$
$h=1.84$ $yards$
