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# The triangular portion of the rectangular lot shown above represents

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Joined: 02 Sep 2009
Posts: 46283
The triangular portion of the rectangular lot shown above represents [#permalink]

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05 Oct 2017, 01:43
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Difficulty:

35% (medium)

Question Stats:

74% (01:09) correct 26% (02:01) wrong based on 42 sessions

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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

Attachment:

2017-10-04_1126.png [ 6.1 KiB | Viewed 700 times ]

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

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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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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

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

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09 Oct 2017, 16:53
Bunuel wrote:

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

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.

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

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09 Oct 2017, 20:18
Bunuel wrote:

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

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 $$z = 10$$

*Else use Pythagorean theorem
$$6^2 + 8^2 = z^2$$
$$36 + 64 = z^2$$
$$100 = z^2$$
$$z = 10$$
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The triangular portion of the rectangular lot shown above represents   [#permalink] 09 Oct 2017, 20:18
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