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The triangular portion of the rectangular lot shown above represents

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The triangular portion of the rectangular lot shown above represents [#permalink]

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New post 05 Oct 2017, 01:43
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The triangular portion of the rectangular lot shown above represents a flower bed. If the area of the bed is 24 square yards and x = y + 2, then z equals

(A) √13
(B) 2√13
(C) 6
(D) 8
(E) 10

[Reveal] Spoiler:
Attachment:
2017-10-04_1126.png
2017-10-04_1126.png [ 6.1 KiB | Viewed 395 times ]
[Reveal] Spoiler: OA

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Re: The triangular portion of the rectangular lot shown above represents [#permalink]

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New post 05 Oct 2017, 02:16
Area of flower bed = (1/2)*x*y = 24, or xy=48 ----(1)
also we know that x=y+2 ----(2)
solving eq. (1) and (2), we get y=-8 and y=6, but cannot be negative, so we have y=6 and hence x = y+2 = 8
Now applying Pythagoras theorem, we get: Z^2 = x^2 + y^2 = 8^2 + 6^2 = 64+36 =100
and hence z=10

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Re: The triangular portion of the rectangular lot shown above represents [#permalink]

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New post 05 Oct 2017, 07:35
Area of the triangular bed = 1/2 xy = 24 => xy = 48
x=y+2 =>x-y=2
The triangular flower bed is a right angled triangle.
By Pythagoras theorem, \(x^2+y^2=z^2\)
z=\(\sqrt{x^2+y^2}\) = \(\sqrt{(x-y)^2+2xy}\)
=\(\sqrt{2^2+2*48}\)=\(\sqrt{100}\)
=10

Answer E
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Re: The triangular portion of the rectangular lot shown above represents [#permalink]

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New post 09 Oct 2017, 16:53
Bunuel wrote:
Image
The triangular portion of the rectangular lot shown above represents a flower bed. If the area of the bed is 24 square yards and x = y + 2, then z equals

(A) √13
(B) 2√13
(C) 6
(D) 8
(E) 10

[Reveal] Spoiler:
Attachment:
2017-10-04_1126.png


The flower bed is a right triangle with sides of y yards, x yards, and z yards. We are given that the area of the bed is 24 square yards.

Since area of a triangle is ½ x base x height, we have:

24 = ½(xy)

48 = xy

We also know that x = y + 2, so substituting y + 2 for x in the area equation, we have:

48 = (y+2)y

48 = y^2 + 2y

y^2 + 2y – 48 = 0

(y + 8)(y – 6) = 0

y = -8 or y = 6

Since we cannot have a negative length, y = 6.

We can use the value for y to calculate the value of x.

x = y + 2

x = 6 + 2

x = 8

We can see that 6 and 8 represent two legs of the right triangle, and now we need to determine the length of z, which is the hypotenuse. Knowing that the length of one leg is 6 and the other leg is 8, we know that we have a 6-8-10 right triangle. Thus, the length of z is 10 yards.

Answer: E
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The triangular portion of the rectangular lot shown above represents [#permalink]

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New post 09 Oct 2017, 20:18
Bunuel wrote:
Image
The triangular portion of the rectangular lot shown above represents a flower bed. If the area of the bed is 24 square yards and x = y + 2, then z equals

(A) √13
(B) 2√13
(C) 6
(D) 8
(E) 10

[Reveal] Spoiler:
Attachment:
2017-10-04_1126.png

We know the triangular garden has a 90-degree corner because it is part of a "rectangular" lot.

It's a right triangle.
x = y + 2

Area = \(\frac{(b*h)}{2}\)

24 = \(\frac{y(y+2)}{2}\)

\(48 = y^2+ 2y\)
\(y^2+ 2y - 48 = 0\)
\((y + 8)(y - 6) = 9\)

\(y\) can't be negative
\(y = 6\)
\(x = 8\)

It's a 3-4-5 right triangle*, so \(z = 10\)

Answer E

*Else use Pythagorean theorem
\(6^2 + 8^2 = z^2\)
\(36 + 64 = z^2\)
\(100 = z^2\)
\(z = 10\)

Kudos [?]: 264 [0], given: 552

The triangular portion of the rectangular lot shown above represents   [#permalink] 09 Oct 2017, 20:18
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