Question

23. The length of a rectangle is 7 more than
its breadth. If the perimeter of the
rectangle is 34 cm, find the length and
breadth of the rectangle.
Your answer
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Answer 1

Step-by-step explanation:

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Answer 2

Answer:

Given:-

The length of a rectangle is 7cm more than its breadth. If the perimeter of the rectangle is 34cm, find the length and breadth of the rectangle.

To Find:-

The length and breadth of rectangle.

Note:-

●》Here, we will take some value of length and breadth as per question and then we will find the actual length and breadth measurement by perimeter formula i.e. Perimeter of rectangle = 2 × ( Length + Breadth ).

●》Transposing is also needed for length and breadth be calculated, it is - For finding some unknown values, some known values changed to other side and also signs are changed. For example - Positive becomes Negative, Multiple becomes Divisional.

Solution:-

$\huge\red{Perimeter = 34cm}$

$\huge\red{Breadth = ?, Let \ \ it \ \ be => x}$

$\huge\red{As \ \ per \ \ question, Length = x + 7cm}$

$\huge\red{ \ \ \ \ Their \ \ actual \ \ measurement = ?}$

☆ According to note first point~

▪︎$Perimeter \ \ of \ \ rectangle = 2 × ( Length + Breadth )$

▪︎$34cm = 2 × ( x + 7cm + x )$

▪︎$34cm = 2 × ( 2x + 7cm )$

▪︎$34cm = 2 × 2x + 2 × 7cm$

▪︎$34cm = 4x + 14cm$

☆ According to note second point ( Transposing )~

▪︎$34cm - 14cm = 4x$

▪︎$20cm = 4x$

▪︎$\dfrac{20cm}{4} = x$

☆ After dividing~

▪︎$5cm = x$

▪︎$x = 5cm$

$\huge\pink{So, Breadth = x => 5cm}$

$\huge\pink{ \ \ Length = x + 7cm = 5cm + 7cm => 12cm}$

Checking:-

♤ Let's check for length and breadth that Perimeter of rectangle = 2 × ( Length + Breadth ) or not.

• $Perimeter \ \ of \ \ rectangle = 2 × ( Length + Breadth ) \implies ?$

♤ Applying length and breadth value~

• $34cm = 2 × ( 12cm + 5cm ) \implies ?$

• $34cm = 2 × ( 17cm ) \implies ?$

• $34cm = 2 × 17cm \implies ?$

• $34cm = 34cm \implies ✔$

$\huge\green{Hence, Proved : Breadth = 5cm}$

$\huge\green{ \ \ \ \ Length = 12cm}$

Answer:-

Hence, the value of Breadth = 5cm

• Length = 12cm.

:)