A farmer has a plot of land whose boundary is formed by two perpendicu

Question

A farmer has a plot of land whose boundary is formed by two perpendicular roads and forms a right triangle. The length of the boundary along one of the roads is 2 kilometers (km), the length of the boundary along the other road is b km, the length of the longest side of the boundary is c km, and the area is A km^2.

In the table, select the value that is closest to c and the value that is closest to A so that the values are jointly consistent with the given information. Make only two selections, one in each column.

Sajjad1994 · Accepted Answer

Official Explanation

RO1

The sides of the plot’s boundary that form the right angle of the triangle are 2 km and b km long, and the longest side is c km long. Using the Pythagorean Theorem, \(c^2 = 2^2 + b^2 = 4 + b^2.\) Taking the square root of each side gives \(\sqrt{4+b^2}\). The area of the triangle, A km, can be found using the equation \(\frac{1}{2}(base)(height).\)\(=\frac{1}{2}(b)(2)\) Since A = b, A can be substituted into the previous expression: \(c=\sqrt{4+A^2}\). Using this equation, the value of c can be calculated for each possible value of A. The table below shows the calculations, rounded to the nearest tenth:

Attachment:

3.jpg [ 13.7 KiB | Viewed 14368 times ]

The only one of these values of c that is among the options given is 2.8.

The correct answer is 2.8.

RO2

As shown in the table provided in the analysis for RO1, c = 2.8 corresponds to A = 2.0.

The correct answer is 2.0.

Sumi1010 · Answer

For the right triangular land, with two sides 2 and b , and longest side c - 
Area A = 2xb/2 = b ---(1)
c = sq root (b^2 + 2^2) = sq root ( b^2 + 4) ---(2)

From (1) and (2), 
A = b, 
c = sq root ( A^2 + 4).

If A = 2, then c= sq root (4 + 4) = 2.82 
if A = 2.8, then c= sq root (11.84) = 3.44
if A = 4, then c= sq root (20) = 4.47
...

Thus , 
 A =2
C = 2.8

suchithra · Answer

If B=2 , then we have Area = \frac{1}{2}*2*2 = 2 km2 and C= \sqrt{4+4} = 2\sqrt{2} = 2.8

Therefore C=2.8 and A=2 is the answer.

TarunKumar1234 · Answer

Given, In Right angled triangle, one side = 2, another perpendicular side = b and hypotenuse (longest side) = c

So, Area = A = 1/2 *base *height = 1/2 * 2*b = b.....(equation)

Condition 1: Say A = 2 = b (from above equation), C = Sqrt (b^2 + 2^2)= Sqrt (2^2 + 2^2)= 2*sqrt(2)= 2.8
 So, A = 2 and C= 2.8 (Ans.)

Condition 2: A= 2.8 =b (from above equation), C = Sqrt (b^2 + 2^2) = Sqrt(2.8^2 + 4) = 3.44 (we don't have such value)

Condition 3: A= 4 =b (from above equation), C = Sqrt (b^2 + 2^2) = Sqrt(4^2 + 4) = 4.47 (we don't have such value)

Condition 4: A= 5.7 =b (from above equation), C = Sqrt (b^2 + 2^2) = Sqrt(5.7^2 + 4) = 6.04 (we don't have such value)

Condition 5: A= 8 =b (from above equation), C = Sqrt (b^2 + 2^2) = Sqrt(8^2 + 4) = 8.2 (we don't have such value)

jhavyom · Answer

A farmer has a plot of land whose boundary is formed by two perpendicular roads and forms a right triangle. The length of the boundary along one of the roads is 2 kilometers (km), the length of the boundary along the other road is b km, the length of the longest side of the boundary is c km, and the area is A km2.

The hypotenuse of the triangle = c
The remaining two sides of the triangle = 2 and b
Area = 1/2 * 2 * b
= b

For b = 2
Area will be 2
and hypotenuse (c) will be 
 c = \sqrt{2^2 + b^2} 
 c = 2\sqrt{2} 
= 2.82

Answers are B and A respecively.

rocky620 · Answer

As per the information:

c = Hypotenuse, Let b & 2 be base and height of the right angles triangle

Since Area, a=  \frac{1}{2} *Base*Height =  \frac{1}{2} *b*2 => A=b....... Eq1

c^2  =  b^2  +  h^2 
 c^2  =  b^2  + 4
Replacing b with a From Eq1

c^2  =  a^2  +  4 
 c^2  -  a^2  =  4

We need a pair of values whose difference is 4

2^2  = 4
 2.8^2  = 7.84 
 4^2  = 16
 5.7^2  = 32.49
 8^2  = 64
Only the difference of  2.8^2  and  2^2  is closer to 4 (3.84)

SO, C=2.8 ; A=2

Deepakjhamb · Answer

answer 1 )

c^2 = b^2 + 2^2 and A = 1/2 * b*2 , so A = b

so C = Underroot (b^2+ 4 ) and A=b

now we need to take various values of A and see if some value matches with c accordingly

we start the table :

we get A = 2 C = 2.82
 A=2.8 C=3.44
 A=4 C=4.47
 A=5.7 C=6.04
 A=8 C = 8.24

SO thus we see that only A=2 and C=2.8 In the table fit very closely with the values we get from equation

so answer is A=2 and C=2.8

jabhatta2 · Answer

Hey  avigutman  - was wondering - could you solve this IR question W/O any calculator ?

I dont think it is possible w/o the calculator, given the closeness of the numbers.

using approximation tecniques -- i thougth these pairs were very close

(i)  a = 2.8  and  c = 4

---------

(ii) 
 a = 5.7  and  c = 5.7  (both  a  and  c  could be  5.7 )
IF a = 5.7, then  a^2  should be = approx 30 
c =  \sqrt{a^2 + 4}  =  \sqrt{Approx. 34} 
c =  \sqrt{Approx. 34} , which is close to 6 ish or 5.9 ish 
5..9 ish --  is close to  -- 5.7 as well.

avigutman · Answer

Yes, jabhatta2, I solved it in my head. Here's the thinking I went through:
1. The area of a right triangle is half the product of its legs. Therefore, A=b (granted, the former is a 2-dimensional measurement and the latter is a 1-dimensional measurement, but numerically they're equal).
2. The square of the hypotenuse is equal to the sum of the squares of the legs, so 2^2+A^2 = c^2
3. The hypotenuse MUST be longer than each of the legs, so c MUST be longer than b(=A) --> This eliminates the second option that you were considering,  jabhatta2 .

Then I went to the first option in the answer choices, and wondered what a A=2 would mean for c. Well, then 8 = c^2 so c is 2*root(2) or approximately 2.8. Done.

I got lucky that the first answer worked out for me, but I would have proceeded with the same strategy as I worked through the remaining answer choices, and I would have used the calculator if I had to. In this case, I didn't have to.

mkeshri185 · Answer

What is C here? only two sides of rectangle are B and 2 then what's C it's said it is the lognest side on the boundary. i did not get the image

Bunuel · Answer

The plot of land forms a right triangle because two perpendicular roads create the boundary. One road is 2 km long, and the other is b km long. These two sides of the triangle form the right angle (90 degrees). The longest side of the triangle, which is opposite the right angle, is the hypotenuse, and that's denoted as c. This hypotenuse is the boundary along the diagonal, connecting the ends of the two roads. https://gmatclub.com/forum/download/file.php?id=86660 GMAT-Club-Forum-d9wexc2r.png

A farmer has a plot of land whose boundary is formed by two perpendicu

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