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Flower bed area

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by kobel51 » Mon Feb 24, 2014 2:27 pm
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The shaded 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) root(13)

B) 2*root(13)

C) 6

D) 8

E) 10
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by Patrick_GMATFix » Mon Feb 24, 2014 2:43 pm
When in doubt about a geometry question, draw and label the figure, identify what you're asked for, write out the relevant formulas and insert all the known values. Taking these steps will generally make obvious what you can solve for.

The full solution below is taken from the GMATFix App.

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by Bill@VeritasPrep » Mon Feb 24, 2014 3:03 pm
Since it's a triangle, A = (bh)/2.

We can use y as the base and y+2 as the height (since x=y+2).

(y(y+2))/2=24

y^2 + 2y = 48

y^2 + 2y - 48 = 0

(y + 8) (y - 6)

So, y must be 6 (since we can't have a side length of -8), making x 8, and z must be 10 to complete the 3-4-5 right triangle.
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by [email protected] » Mon Feb 24, 2014 6:53 pm
Hi kobel51,

On certain GMAT questions, you can "brute force" the work and quickly come up with the correct answer. Here's how:

From the prompt and the picture, we know that...
1) The triangle is a right triangle (because it's in the "corner" of a rectangle)
2) The two legs of the triangle differ by 2
3) The area of the triangle is 24 (A = (1/2)(B)(H))

Let's focus on the area = 24 for a moment. We know the two legs differ by 2, so we can probably "brute force" the possibilities and find the match:

If the legs are:
2 and 4, then the area = 4
4 and 6, then the area = 12
6 and 8, then the area = 24 ---> that's THE match

If the legs are 6 and 8, then we can use the Pythagorean Formula to figure out the value of Z. You might also recognize the "Pythagorean Triplet" and solve the problem that way.

Final Answer: E

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by GMATGuruNY » Tue Feb 25, 2014 4:22 am
kobel51 wrote:Image
The shaded 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) root(13)

B) 2*root(13)

C) 6

D) 8

E) 10
ALWAYS KEEP YOUR EYES ON THE ANSWER CHOICES.
C, D and E imply the sides of a 6-8-10 triangle.
Check whether this triangle satisfies the constraints in the problem:
Image
The area of the triangle above = (1/2)(6)(8) = 24.
Success!
Thus, z=10.

The correct answer is E.
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by Scott@TargetTestPrep » Wed Jul 08, 2015 4:52 am
kobel51 wrote:Image
The shaded 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) root(13)

B) 2*root(13)

C) 6

D) 8

E) 10

Solution:
In solving this problem we first must recognize that the flower bed is the right triangle with sides of x yards, y yards, and z yards. We are given that the area of the bed (which is the right triangle) is 24 square yards. Since we know that area of a triangle is ½ Base x Height, we can say:

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.

If you didn't recognize that 6, 8, and 10 are the sides of a right triangle, you would have had to use the Pythagorean Theorem to find z, the length of the hypotenuse:

6^2 + 8^2 = z^2

36 + 64 = z^2

100 = z^2

The positive square root of 100 is 10, and thus the value of z is 10.

Answer: E

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