Question

Challenge The figure shown is composed of a triangle and a rectangle. The figure has a total area of 1258 square units. Find the value of x.

Short answer

The value of x is 10.09 units

Step-by-step solution

Step-1 – Given

The total area is 1258 square units. The given figure is composed of a triangle with base $3x+1$units and height 24 units and a rectangle with$3x+1$ units width and 25 units length.

Step-2 – To determine

We have to find the value of the x for the given figure.

Step-3 – Calculation

The total area is given by the equation,

$\begin{array}{l}25(3x+1)+\frac{1}{2}\times (3x+1)\times 2=1258\\ 75x+25+36x+12=1258\left[\text{distributiveproperty}\right]\\ 121x+37=1258\left[\text{combineliketerms}\right]\\ 121x+37-37=1258-37\left[\text{subtract37fromeachside}\right]\\ 121x=1221\\ 121x÷121=1221÷121\left[\text{divideeachsidewithby121}\right]\\ x=10.09\end{array}$

Hence, the required value of x for the given figure is 10.09 units.