Final answer:
To find the length and breadth of the field given the perimeter and area, we can set up a system of equations and solve for the unknowns. The length of the field is 10 m and the breadth is 40 m.
Step-by-step explanation:
To find the length and breadth of the field, we can set up a system of equations using the given information. Let's assume the length of the field is 'L' and the breadth is 'B'.
From the given information, we know that 2L + 2B = 100 (perimeter formula) and LB = 5600 (area formula).
Using these two equations, we can solve for L and B. Solving the first equation for L, we get L = 50 - B. Substituting this value into the second equation, we get (50 - B)B = 5600. Expanding and rearranging the equation, we have B^2 - 50B + 5600 = 0.
This is a quadratic equation, which we can solve to find the values of B. By factoring or using the quadratic formula, we find that the values of B are 40 and 140. Substituting these values back into the equation L = 50 - B, we get the corresponding values of L as 10 and -90. Since length cannot be negative, the length of the field is 10 m and the breadth is 40 m.
Learn more about geometry