A piece of carpet is in the shape of a trapezoid. The top

Question

A piece of carpet is in the shape of a trapezoid. The top measures 50 inches, the bottom measures 70 inches. What is the carpet's perimeter?

(1) The area of the carpet is 450 sq inches.
(2) The height of the carpet is 7.5 inches.

I'll follow up with comments later tonight or tomorrow, and with the answer given, which I don't agree with. : (

Big-O · Answer

I think it is D.

Statement 1.

Area of a trapezoid = (Top * Height) + 2 * (1/2 * height * (bottom-top)) (i.e., the sum of the area of the two triangles, which are right angled and can be solved with x^2 + y^2 = z^2).

If we know the Area, and the Top, and the Bottom, then we're solving for height. And then if we know height, and base (top-bottom/2), then we can figure out the hypotenuse. This assumes that it is a perfect trapezoid, but even if it it skewed (i.e., one triangle is bigger than the other), the perimeter (I  think ) wouldn't change...

 sufficient 

Statement 2. 

Given the above formula, we have area, base, and height. We can then figure out area, and therefore perimeter.

 sufficient 

Again, all of this falls through if triangles with the same base and height can have different perimeters...

rainbow · Answer

According to me triangles with the same base and height can have different perimeters.
I just tried it and got different values.

So will go for E...

anonymousegmat · Answer

rainbow I agree with E but your reasoning is off,

by definition a height is perpendicular to the base... so we can draw the height and move it to the vertices, and then we are dealing with at least one right triangle on either side of the rectangle. because a^2+b^2 can lead to one and only one c^2 it follows that the perimeters of the right triangles can not vary when base and height remain constant. 

to answer this problem we need to know if there are one or two hypotenuses, and the bases of each triangle.

I and II basically give use the same information which leads us to a height
= 7.5. so we've got a. we need to find b1 and b2 so we can find c1 and c2.
without knowing the placement of the two parrallel segments we can't find the b's, so we can't find the c's, therefore we can't find the perimeter. also, we don't know if there are 2 triangles attached to a rectangle, or just 
a rectangle attached to one triangle.

GK_Gmat · Answer

E. 

If we knew that the non-parallel sides are equal then the answer would have been D. Since we don't, the answer is E. 

Stat 1: 
Using the formula for the ar. of a trap. we can find out h. 
Now We can drop 2 perpendiculars from the shorter parallel side to the longer one, giving us a rectangle w/ sides 50 and 7.5 and 2 right triangles w/ p = 7.5. 
However, since we don't know how the remaining 20 (70-50) of the longer side is divided b/w the 2 right triangles, we cannot use pythagorus th. to find the hypotenuse of either triangles (which is equal to the non-parallel sides of the trap); insuff.

Stat 2: Gives us no new info; insuff. 

Had we known how the 20 is divided b/w the 2 right triangles, we could have calculated p and therefore, the perimeter.

anonymousegmat · Answer

agreed. it is important to note thought that a trapezoid need not have two triangles

ben928 · Answer

E is correct. You all put great input thanks! I had thought that if 2 trapezoids had the same area and height, then the perimeters must be equal.

This isn't the case though because obviously triangles and rectangles don't act this way:
triangles: right triangle 4:4:sqrt(32) (4*4)/2 = Area = 8; Perimeter = 8+sqrt(32)
& right triangle 8:2:sqrt(68) (8*2)/2 = Area = 8; Perimeter = 10 + sqrt(64)

Good stuff..

A piece of carpet is in the shape of a trapezoid. The top

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