Question

the length of a rectangle garden is 6m more than thrice it's breadth . if it's perimeter is 100m find the dimention of the garden and area​

Answer 1

Step-by-step explanation:

given that

length of garden is 6m more than 3 of its breadth

perimeter is 100m

to find

dimension of garden and its area

solution

as per given condition

$length= 6m + 3 \: of \: breadth$

$perimeter = 2(l + b)$

hence

$100 = 2(6 + 3b + b)$

$100 - 12 = 8b$

$b = 11$

hence lenth will be

$l = 6 + 3 \times 11$

$l = 39$

$area \: ofrectangle \: = l \times b$

$area = 39 \times 11 \\ = 429 {m}^{2}$

hence

length is 39m

breadth is 11m

and area is 429 sq mtr

Answer 2

To find : dimensions of garden and its area .  

Given : length of a rectangle garden is $6$m more than thrice it's breadth .

            Perimeter = $100\ m$

Solution :

• According to question we are given that  length of a rectangle garden is $6\ m$ more than thrice it's breadth and its perimeter is $100\ m$. We have to find dimensions and area of garden .  

• Let , $x$ be the breadth of garden and $(3x + 6\ m )$ length of rectangle .
• To find  we use following formula -

        Perimeter of garden = $2 ( l + b )$

• Substituting the values we get,

      $100 = 2 ( 3x + 6 + x ) \\100 =2 ( 4x + 6 ) \\50 = 4x + 6 \\4x = 44 \\x = 11$

• Breadth  = $x = 11\ m$ and
• length = $3x + 6 = 3 (11 ) + 6 =39\ m$  
• Now , to find area we use following formula ,
• Area of garden  = $l\times b$

                                   $= 39 \times 11 \\= 429 \ m^{2}$

Hence, length and breadth of rectangular garden is  $39\ m$ and $11\ m$ respectively , and area of rectangle is $429\ m^{2}$ .