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

ingwadlatp

ingwadlatp

Answered question

2022-07-27

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

Answer & Explanation

kamphundg4

kamphundg4

Beginner2022-07-28Added 20 answers

Step 1
Let the required rectangle is ABCD as shown below:

Here, let the length of the rectangle is A B = C D = x
And the width of the rectangle is B C = D A = y
As 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 2
We 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 = 106
Step 3
Now, by putting the value of y = 106, in x = 3 2 y, we can find value of x,
x = 3 2 × 106
x = 159
Therefore, 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

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