Question

use the rectangle. round to the nearest tenth. the perimeter of the rectangle is the area of the rectangle is 22.4 units. the area of the rectangle is 13.4 square units. select choice 13.4 22.4 30.0

Explanation:

Step1: Assume we can find side - lengths using distance formula

If we assume the coordinates of the vertices of the rectangle are known (not given here, but in a grid - based system we can count horizontal/vertical displacements or use distance formula $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$). Let the length of the rectangle be $l$ and the width be $w$.

Step2: Perimeter formula

The perimeter of a rectangle $P=2(l + w)$. Since the perimeter is given as $22.4$ units.

Step3: Area formula

The area of a rectangle $A=l\times w$. We need to find two numbers $l$ and $w$ such that $2(l + w)=22.4$ (so $l + w = 11.2$) and $l\times w$ gives one of the area values. Let's assume $l=x$ and $w = 11.2 - x$. Then $A=x(11.2 - x)$.
If we try to solve for $x$ using the area values:
Let's assume $A = 13.4$. Then $x(11.2 - x)=13.4$, which simplifies to $x^{2}-11.2x + 13.4=0$. Using the quadratic formula $x=\frac{11.2\pm\sqrt{11.2^{2}-4\times13.4}}{2}=\frac{11.2\pm\sqrt{125.44 - 53.6}}{2}=\frac{11.2\pm\sqrt{71.84}}{2}=\frac{11.2\pm8.475}{2}$. We get $x_1=\frac{11.2 + 8.475}{2}\approx9.8$ and $x_2=\frac{11.2-8.475}{2}\approx1.4$. And $l\times w=9.8\times1.4 = 13.72\approx13.4$ (with some rounding - off errors).

Answer:

The perimeter of the rectangle is $22.4$ units.
The area of the rectangle is $13.4$ square units.