Question

What is the perimeter of parallelogram RSTU, rounded to the nearest whole number? ​

Answer 1

Given:

The vertices of the parallelogram RSTU are R(-4,4), S(2,6), T(6,2) and U(0,0).

To find:

The perimeter of parallelogram RSTU, rounded to the nearest whole number.

Solution:

Distance formula:

$D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Using the distance formula, we get

$RS=\sqrt{(2-(-4))^2+(6-4)^2}$

$RS=\sqrt{(6)^2+(2)^2}$

$RS=\sqrt{36+4}$

$RS=\sqrt{40}$

$RS=6.32$

Similarly,

$ST=\sqrt{\left(6-2\right)^2+\left(2-6\right)^2}$

$ST\approx 5.66$

$TU=\sqrt{\left(0-6\right)^2+\left(0-2\right)^2}$

$TU\approx 6.32$

$RU=\sqrt{\left(0-\left(-4\right)\right)^2+\left(0-4\right)^2}$

$RU\approx 5.66$

Now, the perimeter of the parabola is:

$P=RS+ST+TU+RU$

$P=6.32+5.66+6.32+5.66$

$P=23.96$

$P\approx 24$

The perimeter of the parallelogram RSTU is 24 units.

Therefore, the correct option is C.

Note: Unit of perimeter cannot be in square.