The length and width of a rectangular lot are in hte ratio 3 to 2. If the perimeter of the lot is 530 yards, find the length and width.Length ? yardsWidth ? yards

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kamphundg4 · Accepted Answer

Step 1Let the required rectangle is ABCD as shown below:Here, let the length of the rectangle is   A  B  =  C  D  =  xAnd the width of the rectangle is   B  C  =  D  A  =  yAs is the question, it is given that the length and width of rectangle are in the ratio of 3 to 2  ⇒  x  :  y  =  3  :  2  ⇒      x    y    =      3    2    (  1  )In the question it is given that perimeter of the rectangular is 530 yards.Step 2We know that,the perimeter of a rectangle is equal to the sum of its all sides. So  A  B  +  B  C  +  C  D  +  D  A  =  530  ⇒  x  +  y  +  x  +  y  =  530  ⇒  2  x  +  2  y  =  530  ⇒  2  (  x  +  y  )  =  530  ⇒  x  +  y  =  265  (  2  )Now, from equation (1) we can write   x  =      3    2    y, but this value of x in the equation (2).  ⇒      3    2    y  +  y  =  265  ⇒            3      y      +      2      y        2    =  265  ⇒            5      y        2    =  265  ⇒  y  =      2    5    ×  265  =  106Step 3Now, by putting the value of   y  =  106, in   x  =      3    2    y, we can find value of x,  ⇒  x  =      3    2    ×  106  ⇒  x  =  159Therefore, the length of the rectangle is   A  B  =  C  D  =  159 yards and the width of the rectangle is   B  C  =  D  A  =  106 yards

The length and width of a rectangular lot are in hte ratio 3 to 2. If the perimeter of the lot is 530 yards, find the length and width. Length ? yards. Width ? yards

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