Peter kept his pony in a rectangular paddock the perimeter of which was 240 metres and the area was 3200 square metres. What were the dimensions of the paddock?
you know that length + width = 120m
So just for grins, what are the factors of 32 which add up to 12?
Now, what are the factors of 3200 which add up to 120?
The factors of 32 are 8 and 4, since they add up to 12 anyways..
And so... the factors for 3200 are both 100 and 20 AND 40 and 80
wait.. where did 120metres come from?
sorry my head is a bit muddle up today... I would've been able to solve it
perimeter is 2(length+width)
To find the dimensions of the rectangular paddock, we can solve a system of equations using the given information.
Let's represent the length of the paddock as "l" and the width as "w".
According to the problem, the perimeter of the paddock is 240 meters. The formula for the perimeter of a rectangle is given by 2(l + w), so we can write the equation:
2(l + w) = 240
Next, we are given that the area of the paddock is 3200 square meters. The formula for the area of a rectangle is given by lw, so we can write the equation:
lw = 3200
Now we have a system of two equations:
2(l + w) = 240
lw = 3200
We can solve this system by substitution or elimination.
Let's use the substitution method. Solve the first equation for l:
l = (240 - 2w) / 2
l = 120 - w
Now substitute this value of l in the second equation:
(120 - w)w = 3200
Expand and rearrange to solve for w:
120w - w^2 = 3200
w^2 - 120w + 3200 = 0
This is a quadratic equation in the form of ax^2 + bx + c = 0, where a = 1, b = -120, and c = 3200. We can solve this quadratic equation by factoring or using the quadratic formula.
Let's use factoring. Find two numbers whose product is ac (3200) and sum is b (-120):
The numbers are -80 and -40:
-80 * -40 = 3200
-80 + (-40) = -120
Now rewrite the quadratic equation:
w^2 - 80w - 40w + 3200 = 0
Factor by grouping:
w(w - 80) - 40(w - 80) = 0
(w - 40)(w - 80) = 0
Setting each factor to zero:
w - 40 = 0 or w - 80 = 0
Solve for w:
w = 40 or w = 80
If w = 40, substitute it into the first equation:
l = 120 - w
l = 120 - 40
l = 80
If w = 80, substitute it into the first equation:
l = 120 - w
l = 120 - 80
l = 40
Therefore, we have two possible pairs of dimensions for the paddock: 40m x 80m or 80m x 40m.