
By: JessicaTan (offline) Tuesday, October 16 2012 @ 01:21 AM CDT (Read 1017 times)



JessicaTan 
Hi, kindly someone help with these two problems with working solution.
attached file
ans for Q16 15.75cm and Q18 105cm

Regular Member
Registered: 10/17/09 Posts: 82





By: echeewh (offline) Wednesday, October 17 2012 @ 09:49 PM CDT



echeewh 
Hi Jessica,
Following is my worked solution for Q16. Q18 to be posted later.
Q16
Vol (V) = Area (A) × Height (H)
Given that base area (A) is constant,
V is proportional to H
H1 (at first) = (2/5) filled = (6/15)
H2 (after added 2362.5 cm3) = (2/3) filled = (10/15)
Using method of proportions,
10u  6u > 2362.5 cm3
4u > 2362.5
6u > 3543.75 (Vol at first)
Height of fruit juice (at first) = (Vol at first) ÷ A
= 3543.75 ÷ (15 × 15)
= 15.75 cm
=============================
Trust this helps.
Do let me know again if there's any clarification.
Cheers,
Edward

Active Member
Registered: 04/21/11 Posts: 627





By: echeewh (offline) Monday, October 22 2012 @ 08:03 PM CDT



echeewh 
hey Jessica,
<23 Oct  posted solution to Q18>
Following pls find my worked solution :
Let length of rectangle = l and breadth of rectangle = b
P of rectangle = 2 (l + b) = 78 = 2l + 2b  (1)
A of rectangle = l × b = 324  (2)
Label triangles W, X, Y and Z (from left to right)
base(W) + base(X) + base(Y) + base(Z) = l (length of rectangle)
P (Perimeter) that makes up 2 sides of each triangle W, X, Y and Z (at top of figure) = 2l
so, P of figure = 2l + 2b + l = 78 + l  (3)
From (1):
l + b = 78 ÷ 2 = 39
b = (39  l)
in (2):
l × (39  l) = 324
39l  (l × l) = 324
(l × l)  39l + 324 = 0
<this is known as quadratic equation>
<process>
What to do here is find factors of 324 and sum of these 2 factors is 39
(l  27)(l  12) = 0
l = 27, 12
if l = 27, then b = 12, since A = 27 x 12 = 324 and P = 2 × (27 + 12) = 2 × 39 = 78 (these are Area & Perimeter of the rectangle)
in (3):
P of figure = 78 + l = 78 + 27 = 105 cm
=====================
Trust this helps.
Do let me know if there's further clarification.
Cheers,
Edward

Active Member
Registered: 04/21/11 Posts: 627



