Mathematics

Grade6

Easy

Question

# Find the perimeter of the rectangle whose coordinates are A (10, 10), B (10, 26), C (45, 26), D (45, 10)

- 560
- 102
- 56
- 260

Hint:

### We are given 4 coordinates of corner of a rectangle ABCD. We are asked to find the perimeter of the rectangle. Perimeter means the length of the boundary of the shape. To solve this question, we will find any two adjacent sides. Once we find the adjacent sides, we will use the formula for perimeter of a rectangle.

## The correct answer is: 102

### The given rectangle is ABCD

The points are:

A = (10,10)

B = (10,26)

C = (45,26)

D = (45,10)

We can consider the length of any two adjacent sides.

Let AB be the length and BC be the breadth.

Let’s find the distance of the side AB

AB has x coordinate same. And the y coordinate has same sign. So the points are in the same quadrant.

We will find the absolute values of the points A and B. Absolute value is distance of the point from respective axis. Here x coordinate is same. So, absolute distance is from x axis.

Absolute distance of the point A is |10|

Absolute distance of the point B is |26|

As both of them are in same quadrant we will have to subtract their absolute distance to find the value of its length.

Length of AB = |26| - |10|

= 26 – 10

= 16 units.

Length of side AB is 16 units

Let’s find the distance of the side BC

BC has y coordinate same. And x coordinate has the same sign. So the points are in same quadrant.

We will find the absolute distance of the points B and C. Here y coordinate is same. So, we will measure distance from y axis.

Absolute distance of the point B is |10|

Absolute distance of the point C is |45|

As both of them are in same quadrant, we will have to subtract their absolute distances to find the value of its length

Length of BC = |45| - |10|

= 45 – 10

= 35 units

Length of side BC is 35 units.

We will find the perimeter now

Perimeter of rectangle ABCD = 2(length + breadth)

= 2(AB + BC)

= 2(35 + 16)

= 2(51)

= 102 units.

Therefore, perimeter of the rectangle ABCD is 102.

We can use distance formula to find the distance too. We have to be careful when finding the absolute values. We have to see which coordinates are same. And the signs of the coordinates.