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 By: JessicaTan (offline)  Tuesday, October 16 2012 @ 01:21 AM CDT (Read 1033 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

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