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Geometry

by MBA.Aspirant » Tue Jun 07, 2011 12:59 pm
The area of a rectangular garden would be increased by 150 square feet if either the length were increased by 7.5 feet or the width were increased by 5 feet. What is the area of the garden, in square feet?

(A) 600 (B) 525 (C) 375 (D) 300 (E) 225
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by MBA.Aspirant » Tue Jun 07, 2011 1:07 pm
Another one:

A square board that has an area of 25 square inches is to be cut into pieces, each of which is a square with sides of length 1, 2, or 3 inches. What is the least number of such square pieces into which the board can be cut?

(A) 5 (B) 6 (C) 7 (D) 8 (E) 9
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by MBA.Aspirant » Tue Jun 07, 2011 1:18 pm
I got the first one:

A = L * W


L+7.5 * W = A+150

LW + 7.5W = LW +150

7.5W = 150

W= 20


L *(W+5) = a +150

LW + 5L = LW +150

5L = 150

L= 30

A= L*w = 20*30 = 600

Answer is A
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by Frankenstein » Tue Jun 07, 2011 1:24 pm
Hi,
Q1) Keeping width(w) constant, length(l) increased by 7.5 increases area by 150. So 7.5*w=150 =>w=20
Keeping length(l) constant, width(w) increased by 5 increases area by 150. So l*5=150 =>l=20
So, Area of garden =l*w = 30*20 = 600sq ft

Hence, A

Q2)No. of 3x3 squares that can be cut = 1(from a corner) --> 9 sq.inches
From the remaining part (16sq.inches), 4 (2x2) cannot be cut.
So, no. of 2x2 squares that can be cut = 3(from remaining part)-->3*(2*2)=12 sq.inches
That leaves 4sq units i.e. 4 (1x1) squares
So, total=1+3+4 = 8

Hence, D
Last edited by Frankenstein on Tue Jun 07, 2011 9:14 pm, edited 1 time in total.
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by MBA.Aspirant » Tue Jun 07, 2011 2:04 pm
Thanks but I don't quite get the 2nd one. Anyway here's another one:

Image


Any quick way to solve this? As it'll take some time to point each side size and do pythagoras
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by MBA.Aspirant » Tue Jun 07, 2011 2:21 pm
Another one:


Image


I don't get the notations on the sides.. is the ABC side = 60 or 60+30?
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by cans » Tue Jun 07, 2011 7:54 pm
The area of a rectangular garden would be increased by 150 square feet if either the length were increased by 7.5 feet or the width were increased by 5 feet. What is the area of the garden, in square feet?

(A) 600 (B) 525 (C) 375 (D) 300 (E) 225
l,w,a means length, width and initial area respectively
w(l+7.5) = a+150
lw=a
this w*7.5=150 ->w=20
similarly l(w+5)=150+a -> l=30
area=30*20=600
IMO A
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by cans » Tue Jun 07, 2011 8:02 pm
A square board that has an area of 25 square inches is to be cut into pieces, each of which is a square with sides of length 1, 2, or 3 inches. What is the least number of such square pieces into which the board can be cut?

(A) 5 (B) 6 (C) 7 (D) 8 (E) 9
area=25. thus side=5
to find least no. of squares, we should use maximum side which is 3.
one 3*3 square. 3 2*2 squares. 4 1*1 squares
total=8
IMO E
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by vikram4689 » Tue Jun 07, 2011 8:08 pm
Man you asked so many questions in 1 post ;)....ill post the answer, do tell for which of them u need explanations.

1)A-600
2)D-8
3)C-3.6 .... mark the co-ordinates and use distance formula (2,6,) (5,-1) (-7,-6)
4)E-1/4 .... ratio of area = ratio of sides*ratio of sides ( ques has an error it should show that both verticals are perpendiculars)
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by cans » Tue Jun 07, 2011 8:12 pm
MBA.Aspirant wrote: Image


Any quick way to solve this? As it'll take some time to point each side size and do pythagoras
if we move the triangle ABC up by 0.1 in vertical direction,
A will be (-0.7,-0.5); B(0.5,0); C(.2,.7)
Also it looks like Right angled triangle to me.
AB^2 = 1.2^2 + 0.5^2 -> AB=1.3
BC^2 = .3^2 + .7^2 ->BC=root(.58)=.75
AC^2 = .9^2 + 1.2^2 = 2.25 -> AC=1.5
Thus perimeter = 2.8+.75 = 3.55 = 3.6
IMO C
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by cans » Tue Jun 07, 2011 8:19 pm
MBA.Aspirant wrote:Another one:


Image


I don't get the notations on the sides.. is the ABC side = 60 or 60+30?
let shorter triangle be BDE
thus BD/BC = DE/AC ->DE/AC=1/2
area BDE/Area ABC = (1/2)(BD)(DE) / (1/2)(AC)(BC) = 1/4
IMO D
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by MBA.Aspirant » Wed Jun 08, 2011 9:07 am
cans wrote:
MBA.Aspirant wrote:Another one:


Image


I don't get the notations on the sides.. is the ABC side = 60 or 60+30?
let shorter triangle be BDE
thus BD/BC = DE/AC ->DE/AC=1/2
area BDE/Area ABC = (1/2)(BD)(DE) / (1/2)(AC)(BC) = 1/4
IMO D
That's a good way to look at it. I calculated it using the areas.

Small triangle base = 30/root3 = 10 root3

Area = 1/2 * 10 root3 * 30 = 150 root 3

Big triangle base = 20 root 3

Area = 1/2 * 20 root 3 * 60= 600 root 3

Ratio of areas = 150 root3/ 600 root 3 = 1/4
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by vikram4689 » Wed Jun 08, 2011 5:09 pm
@cans: i think the ques should mentioned that both verticals are perpendiculars, unless we cannot unless property of SIMILAR TRIANGLES.
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by cans » Wed Jun 08, 2011 8:13 pm
vikram4689 wrote:@cans: i think the ques should mentioned that both verticals are perpendiculars, unless we cannot unless property of SIMILAR TRIANGLES.
Yeah either perpendiculars or that both vertical lines are parallel
But this is problem solving question and we can't solve any other way. Thus I assumed that.
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by phanideepak » Wed Jun 08, 2011 8:36 pm
MBA.Aspirant wrote:Another one:


Image


I don't get the notations on the sides.. is the ABC side = 60 or 60+30?
These are similar triangles so ratio of sides is the same and the ratio of any two sides here = 1/2

area = (1/2 * 30 * DE)/(1/2 * 60 * AC) = 1/4 since DE/AC = 1/2

IMO answer is [spoiler]1/4[/spoiler]
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