Question

A rectangle's length y is half the square of it's width x. The perimeter is 48m. What are the rectangle's dimensions?

Answer 1

Answer:

Given,

y=x^2/2                                                                       ......(i)

perimeter=2(y+x)=48m

y+x=24m                                                                     ......(ii)

substituting (i) in (ii),we get,

(x^2/2)+x=24

x^2+2x=48

x^2+2x-48=0

By splitting the middle term

x^2-6x+8x-48=0

x[x-6]+8[x-6]=0

[x-6][x+8]=0

x=6 or x=-8

but dimension of  rectangle can never be negative.so-8 is impossible

thus x=width=6m

now,

y=x^2/2

y=6^2/2

y=36/2

y=length=18m