Question

this question has two parts. first, answer part a. then, answer part b. part a two vertices of square abcd are c(5, 8) and d(2, 4). a. do you need to find the coordinates for the other two vertices to find the perimeter and area of the square? justify your argument. select choice ; the perimeter and area of a square select choice be found using the length of just one side. select choice yes no b. find the perimeter and area of square abcd. show your work. cd = units p = 4( ) = units a = ( )² = square units

Explanation:

Step1: Determine if other vertices are needed

The perimeter $P = 4s$ and area $A=s^{2}$ of a square are based on side - length $s$. Given two vertices of a square, we can find the side - length between them. So, we do not need to find the other two vertices.

Step2: Calculate the length of side CD

Use the distance formula $d=\sqrt{(x_2 - x_1)^{2}+(y_2 - y_1)^{2}}$. For points $C(5,8)$ and $D(2,4)$, let $(x_1,y_1)=(5,8)$ and $(x_2,y_2)=(2,4)$. Then $CD=\sqrt{(2 - 5)^{2}+(4 - 8)^{2}}=\sqrt{(-3)^{2}+(-4)^{2}}=\sqrt{9 + 16}=\sqrt{25}=5$ units.

Step3: Calculate the perimeter

The perimeter formula for a square is $P = 4s$. Substituting $s = 5$ into the formula, we get $P=4\times5 = 20$ units.

Step4: Calculate the area

The area formula for a square is $A=s^{2}$. Substituting $s = 5$ into the formula, we get $A = 5^{2}=25$ square units.

Answer:

a. No; the perimeter and area of a square can be found using the length of just one side.
b.
$CD = 5$ units
$P=4(5)=20$ units
$A=(5)^{2}=25$ square units