Question

A rectangle field has an area of 300 square meters and a perimeter of 80 meters.what is the ratio of the length to the width of this field

Answer 1

Answer:

Step-by-step explanation:

Let x be the length and y the breadth of the field.

Area = x * y = 300 => y = 300/x --- (i).

Perimeter = 2(x + y) = 80

=> x + y = 40   ---- (ii)

//substitute (i) in place of y.

=> x + 300/x = 40  

=> x² + 300 = 40x

=> x² - 40x + 300 = 0

//now factorize the above quadratic equation

=> x² - 30x - 10x  + 300 = 0

=> x(x - 30) - 10 (x - 30) = 0

=> (x - 30) (x - 10) = 0

=> x = 30m  or 10m.

So when length is 30m, then breadth is 40 - 30 = 10m

    When length is 10m then breadth is 40 - 10 = 30m.

Thus the ratio of length to breadth is 3 : 1  or 1 : 3.