Question

Here is rectangle QRST.

Answer 1

Answers with step-by-step explanation:

We are given the following coordinates of the rectangle QRST:

Q (-3, 0)

R (0, 4)

S (8, -2)

T (5, -6)

QR = $\sqrt { ( 4 - 0 ) ^ 2 + ( 0 - ( - 3 ) ) ^ 2 } = \sqrt { 1 6 + 9 } = \sqrt { 2 5 }$ = 5 units

RS = $\sqrt { ( 4 - ( - 2 ) ) ^ 2 + ( 0 - 8 ) ^ 2} = \sqrt { 3 6 + 6 4 } =\sqrt{100}$ = 10 units

Perimeter of QRST = $2 (QR+RS) = 2(5+10)$ = 30 units

Answer 2

Answer:

QR = 5 units

RS = 10 units

Perimeter of QRST = 30 units

Step-by-step explanation:

The perimeter of a rectangle is given by the formula:

$p=2(l+w)$

where

$p$ is the perimeter of the rectangle

$l$ is the length of the rectangle

$w$ is the width of the rectangle  

Now, to find the width, QR, and the length, RS, of the rectangle, we are using the distance formula:

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

where

$d$ is the distance

$(x_1,y_1)$ are the coordinates of the first point

$(x_2,y_2)$ are the coordinates of the second point

- For QR:

The first point of QR is Q(-3, 0) and the second is R(0, 4), so $x_1=-3$, $y_1=0$, $x_2=0$, and $y_2=4$.

Replacing values

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

$d=\sqrt{(0-(-3))^{2}+(4-0)^{2}}$

$d=\sqrt{(0+3)^{2}+(4)^{2}}$

$d=\sqrt{3^{2} +4^{2}}$

$d=\sqrt{9+16}$

$d=\sqrt{25}$

$d=5$

- For RS

The first point of RS is R(0, 4) and the second is S(8, -2), so $x_1=0$, $y_1=4$, $x_2=8$, and $y_2=-2$.

Replacing values

$d=\sqrt{(8-0)^{2}+(-2-4)^{2}}$

$d=\sqrt{(8)^{2}+(-6)^{2}}$

$d=\sqrt{64+36}$

$d=\sqrt{100}$

$d=10$

Now that we know that the width QR is 5 units and the length RS is 10 units, we can find the perimeter of our rectangle:

$p=2(l+w)$

$p=2(RS+QR)$

$p=2(10+5)$

$p=2(15)$

$p=30$

We can conclude that QR = 5 units, RS = 10 units, and the perimeter of rectangle QRST is 30 units.