Question

A rectangular field has an area of 1,764 m2. The width of the field is 13 m more than the length. What is the perimeter of the field?

Answer 1

Hello,
Here in France we call length the greater side of a rectangle.
So:
Let a the greater side
b the shortest

a=b+13
a*b=1764
==>b*(b+13)=1764
==>b²+13b-1764=0
==>b=(-13-85)/2 to exclude
or (b=(-13+85)/2=36 and a=36+13=49)

P=2(a+b)=2(36+49)=170 (m)
Proof:
49-36=13
36*49=1764

Answer 2

170.

Explanation:

We have that A = W*L where A= Area, W= width, L=length and that W = 13+L. So,

A = (13+L)*L

1764 = 13L + L^2

L^2 + 13L - 1764 = 0.

We use the general formula in the image where a=1, b=13 and c= -1764.

`L1= \frac{-13+\sqrt[2]{169-4*(-1764)} }{2}`

`L1= \frac{-13+\sqrt[2]{7225} }{2}`

`L1= (-13+85)/(2)`

`L1= 36.`

`L2= \frac{-13-\sqrt[2]{169-4*(-1764)} }{2}`

`L2= (-13-85)/(2)`, this result will be negative and the problem is about length so it doesn't apply for this problem. We use L1= 36.

Then, L=36, W = 13 + 36 = 49. Therefore, the perimeter is 2L+2W = 72+98=170.