Question

Quad. FLAT is a rectangle.

If$\mathrm{TO}=4\mathrm{y}+7$ and $\mathrm{FA}=30$, find the value of y.

Short answer

The value of y is 2.

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 TO for FO and AO.

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

Step 3. Description of step.

Substitute 30 for FA and $4y+7$ for TO into $FA=2TO$ to find the value of TO.

$\begin{array}{c}30=2\left(4y+7\right)\\ 30=8y+14\\ 8y=16\\ y=2\end{array}$

Therefore, the value of y is 2.