question related to area of trapezoid , need help in Q.2

Question

Q.1 Hitori’s rock garden is in the shape of a trapezoid. The garden has an area of 60 m2 and a depth of 8 m. The front width is double the back width.
Without changing the front or back widths, by how much must Hitori increase the depth of his garden to double its area?

Q.2 . Refer to question 1. a) Solve this problem using a different method. b) Compare the methods. Describe at least one advantage and one disadvantage of each approach.

i have done Q 1 and solution is given below , need help in Q.2 

(w+2w)/2  * h = Area

3w/2 * h = Area

if w doesn't change, to double A, h must be doubled. 

2  * 3w/2 * h = 2 Area

now need help in Q.2

 

 

Answer 1

Another way to solve this problem is to consider the area to be made of one rectangle and two triangles. If the shorter width is w, the longer width is 2w. If the base of one of the triangles is x, then the base of the other is 2w-x. Area of rectangle=8w because the sides of the rectangle are 8 and w metres. The areas of the triangles are ½(8x)=4x and ½(8*(2w-x))=4(2w-x). Add these areas together: 8w+4x+8w-4x=16w, so 16w=60 sq m and w=15/4=3.75m. If we double the area and keep w the same and replace 8 by h, we get 2hw=120. So h=120/2w=60/w=60/3.75=16m, double the original depth of 8m.

The disadvantage of this method is that it's longer than the other method. The advantage is that it is not formulaic, doesn't use the formula for finding the area of a trapezoid. This is because it breaks down the figure into simpler figures for which area can be calculated from first principles. So it is an intuitive method, compared with a formulaic method. It also shows why the placement of the triangles is irrelevant, because of the terms 4x which cancel out, x being the length of the base of one triangle.

Comments

thank you so much sir