Answer
5.555 cm height, 15.11 cm base
Work Step by Step
$b*h*1/2=A$
$(2x+4)*x*1/2=A$
$(2x^2+4x)*1/2=42$
$x^2+2x=42$
$x^2+2x-42=0$
$x=(-b±\sqrt {b^2-4ac})/2a$
$x=(-2±\sqrt {2^2-4*1*-42})/2*1$
$x=(-2±\sqrt {4+168})/2$
$x=(-2±\sqrt {172})/2$
We are talking about distances, so we want the positive square root.
$x=(-2+\sqrt {172})/2$
$x=(-2+13.11)/2$
$x=11.11/2$
$x=5.555$
$2x+4$
$2*5.555+4$
$11.11+4$
$15.11$
