Chapter 5.7, Problem 20PSB

To determine

Tocalculate: thearea of the given rectangle.

Answer to Problem 20PSB

Area of the rectangle is $33{\text{ units}}^2$

Explanation of Solution

Given information:

One vertex of the rectangle is at $\left(3,0\right)$ . One line $y=-2x+17$ is passing through another vertex of the rectangle in the given picture.

Formula used:

At $x=x_1$ , $y-\text{coordinate}$ on the line $y=mx+c$ is $y_1=m{x}_1+c$ .

Area of the rectangle $\left(A\right)=length\times breadth=l\times b$

Calculation:

Let the rectangle be $ABCD$

Notice that the point $B\left(x,y\right)$ is one the vertices of rectangle and also lies on the line $y=-2x+17$ .

At $C\left(3,0\right),x=3\Rightarrow y-\text{coordinate}$ is $y=-2\left(3\right)+17=-6+17=11$ .

Therefore, another vertex on the rectangle is $B\left(x,y\right)=\left(3,11\right)$ .

In the rectangle $ABCD$ . The length $\left(DC\right)=3\text{ units}$ , the breadth $\left(BC\right)=11\text{ units}$

Area of the rectangle $ABCD$ is,

  $\begin{array}{c}A=length\times breadth\\ =DC\times BC\\ =3\times 11\\ =33{\text{ units}}^2\end{array}$