MBA20 wrote:
The profile of a wood trough is an isosceles trapezoid, as the figure above shows. If 7.5 square feet of water was poured into
the trough that is flat laid, what is the height of the water level?
(A) 0.25
(B) 0.33
(C) 0.4
(D) 0.5
(E) 0.75
VeritasKarishma can u help?
Attachment:
IMG_0205.jpg [ 2.11 MiB | Viewed 493 times ]
The parallel sides of the trapezoid are 1 and 3 and the height is 1. When we drop the altitudes AP and BQ, the trapezoid is split into 3 areas - a square of side 1 and two 45-45-90 triangles. This we can see in the figure above.
Now, say the height of the water is h. The two triangles will still be isosceles since they will be similar to the larger triangles APD and BQC.
If the height is h, the base will be h too since the triangles will be isosceles.
Area of the trapezoid covered by water = Area of rectangle + Area of two 45-45-90 triangles
= h * 1 + 2*(1/2)*h*h = h^2 + h
Volume of the water = Area of trapezoid * 10 = (h^2 + h) *10 = 7.5
10h^2 + 10h - 7.5 = 0
(h + 15/10)*(h - 5/10) = 0
h = 0.5 feet
Answer (D)
Note that volume should be given as 7.5 cubic ft, not square ft
**Edited to add clarity
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Karishma
Veritas Prep GMAT Instructor
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