Question

The coordinates of a rectangle are (3,0) ,(3-5) ,(-4,0) and (-4,-5) type the answers in the boxes below. 1. what is the length and width of this rectangle? length= units width= units 2. what is the perimeter of the rectangle? perimeter= units 3.what is the area of the rectangle? Area= square units (please help me )

Answer 1

Let the rectangle be ABCD as shown below

AB = CD is the length and AD = BC is the width

We would find the length and width by applying the formula for determining the distance between two points which is expressed as

`\begin{gathered} \text{Distance = }\sqrt[]{(x2-x1)^2+(y2-y1)^2} \\ \text{For AB, } \\ x1\text{ = 3, y1 = 0, x2 = 3, y2 = }-\text{ 5} \\ \text{Distance = }\sqrt[]{(3-3)^2+(-5-0)^2} \\ \text{Distance = }\sqrt[]{0\text{ + 25}}\text{ = }\sqrt[]{25}\text{ = 5} \\ AB\text{ = CD = 5} \\ \text{For BC, } \\ x1\text{ = 3, y1 = - 5} \\ x2\text{ = - 4, y2 = 0} \\ \text{Distance = (}\sqrt[]{(-4-3)^2+(0-5)^2} \\ \text{Distance = }\sqrt[]{-7^2+(-5)^2}\text{ = }\sqrt[\square]{49\text{ +25}} \\ \text{Distance = }\sqrt[]{74} \\ BC\text{ = AD = 8.6} \end{gathered}`

Thus,

1) Length = 5 units

Width = 8.6 units

2) Perimeter = 2(length + width) = 2(5 + 8.6) = 6.8 units

3) Area = length * width = 5 * 8.6 = 43 square units