Perimeter of a rectangle is the total length of the boundary or the sum of all its sides. In other words, it is the distance around the outside of the rectangle.
Let us suppose we take a rectangle of length l and breadth b; then its formula for perimeter is given by
P = 2 (l ⨉ b)
Perimeter with Diagonal
To find the perimeter of a rectangle when given the length of its diagonal, you can use the relationship between the diagonal, length, and width of a rectangle.
Let's denote:
- d as the length of the diagonal
- l as the length of the rectangle
- b as the breadth of the rectangle
The relationship between the diagonal and the sides of the rectangle can be expressed using the Pythagorean theorem:
d2 = l2 + b2
Solving this equation for one of the variables, say l, we get:
l2= d2 − b2
Given the length l and breadth b, the perimeter P of the rectangle is:
P = 2l + 2b
Substitute l = √(d2 − b2) into the perimeter equation:
P = 2\sqrt{d^2 - b^2} + 2b
This formula gives you the perimeter of the rectangle in terms of its diagonal d and breadth b.
Solved Examples
Example 1: Find the perimeter of a rectanglewhose length is 8 cm and breadthis 12 cm.
Solution:
Given, l = 8 and b = 12 cm
So, Substitute both values in perimeter formula,
P = 2(l + b) = 2(12 + 8) = 40 cmTherefore the perimeter of a rectangle whose length is 8 cm and breadth is 12 cm is 40 cm.
Example 2: Find the perimeter of a rectangle whose sides are 2 cm and 4 cm.
Solution:
Given, l = 2 and another side b = 4 cm.
So, Substitute the both values in perimeter formula,
P = 2(l + b) = 2(2 + 4) = 12 cmTherefore, the perimeter of a rectangle whose side is 2 cm and another side is 4 cm is 12 cm.
Example 3: Find the perimeter of a rectangular carrom board whose sides are 10 cm and 20 cm.
Solution:
Given, l = 10 and another side b = 20 cm of the carrom board.
So, Substitute the both values in perimeter formula,
P = 2(l + b) = 2(10 + 20) = 60 cm.Therefore, the perimeter of a rectangular carrom board whose side is 10 cm and another side is 20 cm is 60 cm.
Example 4: Find the perimeter of a bed cot whose sides are 100 cm and 200 cm.
Solution:
Given, l = 100 and another side b = 200 cm of the bed cot.
So, Substitute the both values in perimeter formula,
P = 2(l + b) = 2(100 + 200) = 600 cm.Therefore, the perimeter of a bed cot whose sides are 100 cm and 200 cm is 600 cm.
Example 5: Find the perimeter of a compost pit whose longest side is 100 cm and shortest side is 34 cm.
Solution:
Given, Longest side = 100 cm, so length (l) will be the longest side.
So l = 100 cm.Shortest side = 34 cm, so breadth (b) will be the shortest side.
So b = 34 cmSo, Substitute the both values in perimeter formula,
P = 2(l + b) = 2(100 + 34) = 268 cmTherefore, the perimeter of a compost pit whose longest side is 100 cm and shortest side is 34 cm is 268 cm
Practice Problems on Perimeter of a Rectangle
Question 1: Find the perimeter of a rectangular park whose length is 20 m and breadth is 30 m.
Question 2: If the length of a rectangle is twice its breadth and the perimeter is 36 m then find the length and breadth of the rectangle.
Question 3: If the the Perimeter of a rectangular field is 30 m and its length is 7 m find its breadth.
Question 4: Ram is walking along the boundary of a rectangular field whose length is 20 m and breadth is 60 m. Find the distance covered by Ram in one complete round such that Ram reaches the starting point.
Answer Key
Answer 1: Perimeter of the rectangular park is 100m.
Answer 2: Length and breadth of the rectangle is Length = 12m, Breadth = 6m.
Answer 3: Breadth of the rectangular field is 8m.
Answer 4: Distance covered by Ram in one complete round is 160m.
