The dimensions of the rectangle field, whose length is 5m greater than its width and area 1800 m² is 45×40 meters.
What is the area of a rectangle?
Area of a rectangle is the product of the length of the rectangle and the width of the rectangle. It can be given as,
\(A=a\times b\)
Here, (a)is the length of the rectangle and (b) is the width of the rectangle
Suppose the dimension of the field is x×y, where x is the length and y is the width of the field.
As, the area of the field is 1800 m². Therefore,
\(xy=1800\\x=\dfrac{1800}{y}\) ....1
The length of this field is 5 m greater than its width. Therefore,
\(x=y+5\)
Put the value of x from the equation 1 in the above expression as,
\(\dfrac{1800}{y}=y+5\\y^2+5y-1800=0\\y^2+45y-40y-1800=0\\y(y+45)-40(y+45)=0\\(y+45)(y-40)=0\)
By equation the values, we get the width -45 and 40. As the width can not be negative. Thus, the width of the field is 40 m.
Put this value in equation one as,
\(x=40+5\\x=45\)
Hence, the dimensions of the rectangle field, whose length is 5m greater than its width and area 1800 m² is 45×40 meters.
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