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# A lawnmower has cut a diagonal path across a rectangular patch of gras

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Math Expert
Joined: 02 Sep 2009
Posts: 53066
A lawnmower has cut a diagonal path across a rectangular patch of gras  [#permalink]

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02 Sep 2018, 22:20
1
2
00:00

Difficulty:

25% (medium)

Question Stats:

76% (02:11) correct 24% (02:23) wrong based on 41 sessions

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A lawnmower has cut a diagonal path across a rectangular patch of grass 8 ft. by 10 ft. If the resulting path cut two feet off of each corner it crossed, as shown, what percent of the grass was removed by the lawnmower?

A. 80%
B. 66%
C. 60%
D. 40%
E. 32%

Attachment:

image014.jpg [ 2.23 KiB | Viewed 838 times ]

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Re: A lawnmower has cut a diagonal path across a rectangular patch of gras  [#permalink]

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02 Sep 2018, 22:30
Total area = 80

2 side triangles sum to 4.

2 other triangles have an area 48.

Removed area = 80 - 4 - 48=28

28/80 in % is 35

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A lawnmower has cut a diagonal path across a rectangular patch of gras  [#permalink]

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02 Sep 2018, 22:38
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Bunuel wrote:

A lawnmower has cut a diagonal path across a rectangular patch of grass 8 ft. by 10 ft. If the resulting path cut two feet off of each corner it crossed, as shown, what percent of the grass was removed by the lawnmower?

A. 80%
B. 66%
C. 60%
D. 40%
E. 32%

Attachment:
image014.jpg

OA:D
Drawing Diagonal through Middle of the path, We get 2 triangles on one side of diagonal

Area of Diagonal path$$= 2 * (\frac{1}{2}*10*8-\frac{1}{2}*8*6) = 10*8 - 8*6 = 8*(10-6) = 8*4 =32$$

Area of Rectangular patch$$= 8*10 = 80$$

Ratio of path area to rectangular patch area $$= \frac{32}{80}$$

Percentage of Path area to rectangular patch area $$= \frac{32}{80} *100 =40$$%
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Re: A lawnmower has cut a diagonal path across a rectangular patch of gras  [#permalink]

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03 Sep 2018, 01:47
Given L=10 and B =8
Total Area= l*b=80
shaded area = area of two triangles = remaining grass after the cut =(l-2)(b-2)=8*6=48.
we are asked to find the non shaded area(grass removed area) in the whole rectangular lawn: so 80-48=32.
percent of the grass was removed by the lawnmower:(32)/(80) * 100 = 40
Don't fall in trap choosing 60
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Re: A lawnmower has cut a diagonal path across a rectangular patch of gras  [#permalink]

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03 Sep 2018, 02:08
Bunuel wrote:

A lawnmower has cut a diagonal path across a rectangular patch of grass 8 ft. by 10 ft. If the resulting path cut two feet off of each corner it crossed, as shown, what percent of the grass was removed by the lawnmower?

A. 80%
B. 66%
C. 60%
D. 40%
E. 32%

Attachment:
image014.jpg

% Grass removed by lawnmower = 100 - % Grass remaining = 100 - ((2*(1/2)*8*6)/(10*8)) = 100 - 60 = 40%
Intern
Joined: 16 Jul 2017
Posts: 23
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Re: A lawnmower has cut a diagonal path across a rectangular patch of gras  [#permalink]

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03 Sep 2018, 08:14
Area of the 2 triangles = 48 [2*( 1/2 b*h)]
where, sides 8-2=6 and 10-2=8

Removed area = 80 - 48= 32

removed/ total * 100

=> 32/80 *100 =40%
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Re: A lawnmower has cut a diagonal path across a rectangular patch of gras  [#permalink]

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07 Sep 2018, 16:10
Bunuel wrote:

A lawnmower has cut a diagonal path across a rectangular patch of grass 8 ft. by 10 ft. If the resulting path cut two feet off of each corner it crossed, as shown, what percent of the grass was removed by the lawnmower?

A. 80%
B. 66%
C. 60%
D. 40%
E. 32%

Attachment:
image014.jpg

The area of the rectangular patch is 8 x 10 = 80 sq ft. Instead of finding the area of the patch where grass has been removed, let’s find the area of the patches where grass has not been removed, since it consists of two triangular region of the same area (the shaded regions). Each of these triangles has a base of 10 - 2 = 8 ft and a height of 8 - 2 = 6 ft. Therefore, each has an area of ½ x 8 x 6 = 24 sq ft, and, hence, both together have an area of 2 x 24 = 48 sq ft. That means the area of the patch where grass has been removed is 80 - 48 = 32 sq ft. Therefore, the percent of the grass removed is 32/80 = 4/10 = 40%.

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Re: A lawnmower has cut a diagonal path across a rectangular patch of gras   [#permalink] 07 Sep 2018, 16:10
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