Question

Can someone help me with this problem ​

Answer 1

A = 20

P = 6√10

Explanation:

The formula of a distance between two points:

`d=√((x_2-x_1)^2+(y_2-y_1)^2)`

A(-3, 0) , B(3, 2)

`AB=√((3-(-3))^2+(2-0)^2)=√(6^2+2^2)=√(36+4)=√(40)=√(4\cdot10)=\sqrt4\cdot√(10)=2√(10)`

A(-3, 0), D(-2, -3)

`AD=√((-2-(-3))^2+(-3-0)^2)=√(1^2+(-3)^2)=√(1+9)=√(10)`

AB = CD and AD = BC

The area of a rectangle:

`A=(AB)(AD)`

Substitute:

`A=(2√(10))(√(10))=(2)(10)=20`

The perimeter of a rectangle:

`P=2(AB+AD)`

Substitute:

`P=2(2√(10)+√(10))=2(3√(10))=6√(10)`