**Perimeter of Rectangle :**

In this section, we are going to learn, how to find perimeter of a rectangle.

A rectangle is a four-sided closed figure where the lengths of opposite sides will be equal and each vertex angle will be right angle or 90^{o }as shown below.

Let l be the length and w be the width of a rectangle.

Then, the formula for perimeter of the rectangle :

**Perimeter = 2(l + w)**

**Example 1:**

The length and width of a rectangle are 16 cm and 12 cm respectively. Find its perimeter.

**Solution:**

Formula for perimeter of a rectangle :

= 2(l + w)^{ }

Substitute 16 for l and 12 for w.

= 2(16 + 12)

= 2(28)

= 56

So, the perimeter of the rectangle is 56 cm.

**Example 2:**

If the perimeter of a rectangle is 50 cm and its length is 15 cm, then find its width.

**Solution:**

Perimeter of the rectangle = 50 cm

2(l + w) = 50

Divide each side by 2.

l + w = 25

Substitute 15 for l.

15 + w = 25

Subtract 15 from each side.

w = 10

So, the width of the rectangle is 10 cm.

**Example 3 :**

The area of the rectangle is 150 square inches. If the length is twice the width, then find its perimeter.

**Solution:**

Let x be the width of the rectangle.

Then, the length of the rectangle is 2x.

Area of the rectangle = 150 in^{2}

l ⋅ w = 150

x ⋅ 2x = 150

2x^{2} = 150

Divide each side by 2.

x^{2} = 75

Find positive square root on both sides.

√x^{2 } = √75

x = √(5 ⋅ 5 ⋅ 3)

x = 5√3

Therefor, the width of the rectangle is 5√3 in.

Then, the length of the rectangle is

= 2 ⋅ width

= 2 ⋅ 5√3

= 10√3 in

Formula for perimeter of a rectangle :

= 2(l + w)

Substitute 10√3 for l and 5√3 for w.

= 2(10√3 + 5√3)

= 2(15√3)

= 30√3

So, the perimeter of the rectangle is 30√3 in.

**Example 4:**

The length of a rectangle is 3 ft and one of the diagonal measures √13 ft. Find its perimeter.

**Solution:**

To find the perimeter of a rectangle, we have to know its length and width. Length is given in the question, that is 3 ft. So, find its width.

Draw a sketch.

In the figure shown above, consider the right triangle ABC.

By Pythagorean Theorem, we have

AB^{2} + BC^{2} = AC^{2}

Substitute.

AB^{2} + 3^{2} = (√13)^{2}

Simplify and solve for AB.

AB^{2} + 9 = 13

Subtract 9 from each side.

AB^{2} = 4

Find positive square root on both sides.

√AB^{2} = √4

AB = 2

Therefore, the width of the rectangle is 2 ft.

Formula for perimeter of a rectangle.

= 2(l + w)

Substitute 3 for l and 2 for w.

= 2(3 + 2)

= 2(5)

= 10

So, the perimeter of the rectangle is 10 ft.

**Example 5:**

The length of a rectangle is 3 yards more than its width and its perimeter is 18 yards. Find its length and width.

**Solution:**

Let x be the width of the rectangle.

Then, the length of the rectangle is (x + 3) yards.

Perimeter of the rectangle = 18 yards

2(l + w) = 18

Divide each side by 2.

l + w = 9

Substitute (x + 3) for l and x for w.

(x + 3) + x = 9

x + 3 + x = 9

2x + 3 = 9

Subtract 3 from each side.

2x = 6

Divide each side by 2.

x = 3

x + 3 = 6

So, the length of width of the rectangle are 6 yards and 3 yards respectively.

After having gone through the stuff given above, we hope that the students would have understood, "Perimeter of Rectangle".

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

Widget is loading comments...

You can also visit our following web pages on different stuff in math.

**WORD PROBLEMS**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Trigonometry word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**