Question

What two properties of squares would you use to solve the problembelow? *Given square ABCD, the length of DB is 3/2. Find the following: 1)Find the length of DC2)Find the perimeter of square ABCD.

Answer 1

DC=3

Perimeter=12

Explanation

Step 1

in a squre ,opposite sides are congruent , then

side A= sideB

then

we have a rigth triangle , then

$\begin{gathered} \text{side}^2+side^2_2=hypotenuse^2 \\ as\text{ the sides are equal} \\ 2\cdot side^2=(3\sqrt[]{2})^2 \\ 2\cdot\text{side}^2=9\cdot2 \\ \text{side}^2=\frac{18}{2} \\ \text{side}=\sqrt[]{9} \\ \text{side}=3 \end{gathered}$

in a square ,all sides are congruent, then

$\begin{gathered} \text{side}1=\text{side}2=\text{side}3=\text{side}4 \\ \text{Perimeter}=\text{ 4}\cdot side \\ \text{Perimeter}=4\cdot3 \\ \text{Perimeter}=12 \end{gathered}$

I hope this helps you