Question

Quad. FLAT is a rectangle.

If $\mathrm{FA}=27$find $\mathrm{LO}$.

Short answer

The value of LO is 13.5.

Step-by-step solution

Step 1. Description of step.

The diagonals of the rectangle are equal in length and bisect each other.

Therefore, $TO=LO=FO=AO$.

Step 2. Description of step.

A diagonal FA can be written as $FA=FO+AO$.

Substitute LO for $FO\text{and}AO$.

$\begin{array}{c}FA=LO+LO\\ =2LO\end{array}$

Step 3. Description of step.

Substitute 27 for FA into $FA=2LO$ to find the value of LO.

$\begin{array}{c}27=2LO\\ LO=\frac{27}{2}\\ =13.5\end{array}$

Therefore, the value of LO is 13.5.