Question

the length of a rectangle is 3 more than its width .if the perimeter of the rectangle is 30 cm then find the length and width of the rectangle ​

Answer 1

Question:

• The length of a rectangle is 3 more than its width .if the perimeter of the rectangle is 30 cm then find the length and width of the rectangle ​

Answer:

• The length and width of the rectangle are 6cm and 9cm respectively

Explanation:

Given that:

• The length of a rectangle is 3 more than its width
• the perimeter of the rectangle is 30 cm

To Find:

• The length and width of the rectangle ​

Formula Used:

$\bigstar \; \; {\underline{\boxed{\bf{ Perimeter = 2 ( Length + Breadth )}}}}$  

Required Solution:

• Using formula to find the perimeter of the rectangle

★ We know that ,

${\pink{\bigstar \; \; {\underline{\boxed{\bf{ Perimeter_{(rectangle)} = 2 ( L_{(length)}+ B_{(breadth)} )}}}}}}$

★ Where ,

• Perimeter is considered as the measure of the boundary of an object
• Length is said to be the most extended dimension of the rectangle
• Breadth is referred to the shorter dimension compared to the length also called as width

★ Let us assume that ,

• The breadth of the rectangle is x
• The length of the rectangle is x + 3

According to the question:

• Since we have been provided with the perimeter of the rectangle and said that the length of the rectangle is 3 more than its breadth so , let's use the above mentioned formula to find out the measure of the dimensions the assumptions made

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${\purple{\star \; \; {\underline{\bf{ Substituting \; the \; values \; we \; get :}}}}}$

➻ $\bf Perimeter \; _{(of \; the \; rectangle )}= 2 ( L + B )$

➻ $\bf 30\;cm = 2 ( x + 3 \; cm + x )$

➻ $\bf 30\;cm = 2 ( 2x + 3 \; cm )$

➻ $\bf 30\;cm =4x + 6 \; cm$

➻ $\bf 24 \; cm = 4x$

➻ $\bf x = \cancel\dfrac{24 \; cm}{4}$

➻ ${\red{\bf { x = 6cm }}}$

★  Henceforth ,

• The breadth of the rectangle measures 6cm
• The breadth of the rectangle measures 9cm

Verification:

➸ $\bf Perimeter = 2 ( L + b )$

➸ ${\bf{ 30cm = 2 ( 9cm + 6cm) }}$

➸${\bf{ 30cm = 2 (15cm) }}$

➸ $\bf {\purple{ 30cm = 30cm }}$

L.H.S = R.H.S

${\pink{\boxed{\bf{Hence \; Verified \;\checkmark }}}}$

Therefore:

• The length and width of the rectangle are 6cm and 9cm respectively

Know more:

• Area of a rectangle = Length × Breadth
• Area of a parallelogram = Base × height
• Area of a triangle = 1/2 × Base × height
• Area of a circle = π × radius ²
• Area of a trapezium = 1/2 × ( a + b ) × height

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Answer 2

Solution᭄

Given , Perimeter = 30 cm

Let's width = (x) cm

And length = (x + 3) cm

Perimeter of rectangle = 2 ( l + b )

30 = 2 [(x + 3 ) + (x)]

30 = 2 (2x+ 3 )

30 / 2 = 2x+ 3

2x + 3 = 15

2x = 15 - 3

x = 12/2

x = 6

Therefore , width = 6 cm

And length = 6+3 = 9 cm