Question

In a nearby park, a field has been marked off for the neighborhood Pop Warner football team. If the field has a perimeter of 310 yd and an area of 4950 yd', what are the dimensions of the field?

Answer 1

The dimension of the field is ( 110 x 45)

Exolanations:

Perimeter of the field, P = 310 yd

Area of the field, A = 4950 yd²

Note that the shape of a field is rectangular:

Perimeter of a rectangle, P = 2(L + B)

Area of a rectangle, A = L x B

Substituting the values of the perimeter, P, and the Area, A into the formulae above:

310 = 2(L + B)

310 / 2 = L + B

155 = L + B

L + B = 155...............................................(1)

4950 = L x B...............(2)

From equation (1), make L the subject of the formula:

L = 155 - B...................(3)

Substitute equation (3) into equation (2)

4950 = (155 - B) B

4950 = 155B - B²

B² - 155B + 4950 = 0

Solving the quadratic equation above:

B² - 110B - 45B + 4950 = 0

B (B - 110) - 45(B - 110) = 0

(B - 110) ( B - 45) = 0

B - 110 = 0

B = 110

B - 45 = 0

B = 45

Substitute the value of B into equation (3)

L = 155 - B

L = 155 - 45

L = 110

The dimension of the field is ( 110 x 45)