Question

Length of a rectangle exceeds its breadth by 9m. If the perimeter of the rectangle is 94m, then its length is ____________ *
​

Answer 1

Answer:

$\bigstar{\bold{Length\:of\:the\:rectangle=28\:m}}$

Step-by-step explanation:

$\Large{\underline{\underline{\bf{Given:}}}}$

• Length of the rectangle = Breadth + 9
• Perimeter = 94 m

$\Large{\underline{\underline{\bf{To\:Find:}}}}$

• Length of the rectangle

$\Large{\underline{\underline{\bf{To\:Find:}}}}$

➔ Let the length of the rectangle be l

➔ Let the breadth of the rectangle be b

➔ By given,

    l = b + 9----(1)

➔ The perimeter of a rectangle is given by,

    Perimeter of the rectangle = 2 (l + b)

➔ Substituting the value for area we get,

    94 = 2(l +b)

➔ Substitute the value for l from equation 1

    94 = 2 (b + 9 + b)

    94 = 2 (2b + 9)

    94/2 = 2b + 9

    2b + 9 = 47

    2b = 47 - 9

    2b = 38

      b = 38/2

      b = 19

➔ Hence the breadth of the rectangle is 19 m.

➔ Now substitute the value of b in 1

    l = b + 9

    l = 19 + 9

    l = 28

➔ Hence length of the rectangle is 28 m

    $\boxed{\bold{Length\:of\:the\:rectangle=28\:m}}$

$\Large{\underline{\underline{\bf{Verification:}}}}$

➔ l = b + 9

   28 = 19 + 9

   28 = 28

➔ 2 (l + b) = 94

    2 (28 + 19) = 94

    2 × 47 = 94

    94 = 94

➔ Hence verified.

Answer 2

Answer :-

→ Length of the rectangle = 28 m

________________________________

★ Concept :-

Here the concept of Linear Equations have been used. According to this concept, if the value of one variable is made to depend on other, we can find the value of both the variables.

• Perimeter of Rectangle = 2(Length + Breadth)

_____________________

★ Solution :-

Given,

» Length of the rectangle exceeds its breadth by 9 m

» Perimeter of the rectangle = 94 m

• Let the Length of the rectangle be 'L' m

• Let the Breadth of the rectangle be 'B' m

Then,

________________________________

According to the question :-

~ Case I :-

✒ L = 9 + B .. (i)

~ Case II :-

✒ 2(L + B) = 94

✒ 2L + 2B = 94 ..(ii)

From equation (i) and equation (ii) ,

✒ 2B + 2(9 + B) = 94

✒ 2B + 18 + 2B = 94

✒ 4B = 94 - 18

✒ 4B = 76

✒ $</strong><strong> </strong><strong>\</strong><strong>b</strong><strong>o</strong><strong>l</strong><strong>d</strong><strong>{</strong><strong>Br</strong><strong>e</strong><strong>a</strong><strong>d</strong><strong>t</strong><strong>h</strong><strong>,</strong><strong> </strong><strong>B</strong><strong>}</strong><strong> </strong><strong>\: = \: </strong><strong>\</strong><strong>b</strong><strong>o</strong><strong>l</strong><strong>d</strong><strong>{</strong><strong>\</strong><strong>d</strong><strong>frac{</strong><strong>7</strong><strong>6</strong><strong>}{</strong><strong>4</strong><strong>}</strong><strong>}</strong><strong>$

✒ Breadth = 19

» Hence, we get, Breadth of the rectangle = 19 m

Now using equation (i) , we get,

» Length of Rectangle = 9 + B = 9 + 19

= 28 m

_____________________

★ More to know :-

• Linear Equation is the equation formed by variables and constants. These can be solved by

1. Substitution Method
2. Elimination Method
3. Cross Multiplication
4. Reducing the Pair

_____________________

★ Verification :-

In order to verify, that our answer is correct or not, we must have to apply our result in the equation we formed. Then,

~ Case I :-

=> L = B + 9

=> 28 = 19 + 9 = 28

Clearly, LHS = RHS.

~ Case II :-

=> 2(L + B) = 94

=> 2(28 + 19) = 94

=> 2 × 47 = 94

=> 94 = 94

Clearly, LHS = RHS

Here both the equations satisfy. Hence, our answer is correct.