Chikis Posted September 30, 2014 Posted September 30, 2014 Please I need help with these problem: A rectangular courtyard 8m by 6m has a rectangular lawn of area 12m^2 situated in it in such way as to leave a path x m wide all round the inside of the courtyard. Find the value of x. From the way, I represented the xm wideness all around inside the courtyard, it shows that the area the lawn=(8-2x)m by (6-2x)m = 12m^2 The area of only the lawn = 12m^2 The area of the courtyard = 48 48-12 = 36 The 36m^2 is what area? Is it area of the path?
studiot Posted September 30, 2014 Posted September 30, 2014 (edited) The 36m^2 is what area? Is it area of the path? Yes that is correct. But do you need to know this to solve the problem? Keep going. Edited September 30, 2014 by studiot
Chikis Posted September 30, 2014 Author Posted September 30, 2014 (edited) I don't even have problem finding x. I want to verify something. If the area of path is 36m^2. What is the dimension of the path in terms of x? Edited September 30, 2014 by Chikis
studiot Posted September 30, 2014 Posted September 30, 2014 I don't even have problem finding x. I want to verify something. If the area of path is 36m^2. What is the dimension of the path in terms of x? I don't understand. what dimension of the path? x is the width of the path. The path also has a length and external and internal perimeters, because of its shape. The lawn only has an external perimeter. Both lawn and path have areas, you have found the path area. The path area is the length times x (the width). The length is the distance along the centreline of the path.
Chikis Posted September 30, 2014 Author Posted September 30, 2014 (edited) What I mean is what is the lenght and width of the path such that the area of path = 36m^2 If x is the width of the path. What is the lenght of the path? Edited September 30, 2014 by Chikis
studiot Posted September 30, 2014 Posted September 30, 2014 Area = length times width. You know the area, you know the width so you can calculate the length.
Chikis Posted September 30, 2014 Author Posted September 30, 2014 (edited) The path can be splited into 2 pairs of path. So what are the dimension of the two pairs of path? I want sum up all the areas of the pairs of path to get 36m^2. Edited September 30, 2014 by Chikis
studiot Posted September 30, 2014 Posted September 30, 2014 (edited) Maybe this sketch will help - I keep saying draw a diagram. What did you make x? I have shown the centreline dashed. Alternatively you can calculate as you suggest by splitting the path into two pairs so that you do not count the corner areas twice. So say two 8m strips and two strips of length (6 - 2x) So the total area = 2*8*x + 2*(6-2x)*x This comes to the same as the equation at the bottom of my diagram. Edited September 30, 2014 by studiot
Chikis Posted September 30, 2014 Author Posted September 30, 2014 Thanks for helping me verify what I want to verify. Am now satisfied.
studiot Posted September 30, 2014 Posted September 30, 2014 (edited) Area = length times width. If you think about it, there must be a number that multiplies by the width to make the the area. As I said this is always the length of the centre line, which is why engineers use the centre line to measure things. This is a useful thing to learn, not often taught in maths courses. Edited September 30, 2014 by studiot
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