Answer
$y=28\;cm$.
Work Step by Step
The given values are
Height $h=y$
Bases $b_1=y$ and $b_2=4y$.
Area $A=1960\;cm^2$.
The given formula is
$\Rightarrow A=\frac{1}{2}h(b_1+b_2)$
Substitute all values.
$\Rightarrow 1960\;cm^2=\frac{1}{2}y(y+4y)$
Simplify.
$\Rightarrow 1960\;cm^2=\frac{1}{2}y(5y)$
$\Rightarrow 1960\;cm^2=\frac{5}{2}y^2$
Multiply the equation by $\frac{2}{5}$
$\Rightarrow \frac{2}{5}\cdot 1960\;cm^2=\frac{2}{5}\cdot\frac{5}{2}y^2$
Simplify.
$\Rightarrow 784\;cm^2=y^2$
Take the square root on both sides.
$\Rightarrow \sqrt{784\;cm^2}=\sqrt{y^2}$
Simplify.
$\Rightarrow 28\;cm=y$.
