Question

Quadratics Question

Answer 1

P = 2(l+w)

200 = 2(l+w)

divide by 2 on each side

100 = l+w

let the length = x

100 = x+w

solve for w but subtracting x from each side

100 -x = w

A= l*w

we know l =x

substitute for w  because we found w above 100 -x = w

A =  x * (100-x)

distribute

A = 100x - x^2

10.  if A = 2400

2400 = 100x-x^2

subtract 100x from each side

2400 -100x = 100x-x^2 -100x

2400 -100x = -x^2

add x^2 to each side

2400-100x^2 + x^2 = -x^2 + x^2

x^2 -100x+2400 =0

factor

(x-60) (x-40) = 0

using the zero product property

x-60 = 0    x-40 = 0

x=60    x=40

If x=60  then 100 -x = w  100-60 = w  w=40

If x=40 then 100 -x = w  100-40 = w  w=60

The dimensions are 60m by 40 m