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In rectangle QRST, point P is the midpoint of side RS. If the area of
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19 Jun 2022, 23:54
19 Jun 2022, 23:54
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Question Stats:
75% (01:17) correct
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In rectangle QRST, point P is the midpoint of side RS. If the area of quadrilateral QRPT is 30, what is the area of rectangle QRST?
A. 40
B. 60
C. 80
D. 100
E. 120
A. 40
B. 60
C. 80
D. 100
E. 120
Part of the project: GRE QCQ & PS 3 Questions Every One DAILY Challenge - (2022)
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GRE Math Essentials for a TOP Quant Score - Q170!!! (2021)
GRE Geometry Formulas for a Q170
GRE - Math Book
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
GRE Math Essentials for a TOP Quant Score - Q170!!! (2021)
GRE Geometry Formulas for a Q170
GRE - Math Book
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Re: In rectangle QRST, point P is the midpoint of side RS. If the area of
[#permalink]
20 Jun 2022, 07:50
20 Jun 2022, 07:50
1
This seems like a question that needs drawing, but it's really quite simple if you use the correct equations.
The area of a rectangle is, of course, base*height.
The quadrilateral that would form as QRPT is a trapezoid because it has two parallel sides and two non-parallel sides. The area of a trapezoid is this:
((base_1 + base_2)/2) * height
Now, if we look at the trapezoid, using p as the midpoint of side RS, we see that base_1 will be exactly half of base_2. Let's call base_1 = x, which makes base_2 = 2x. For good measure, let's call the height = h.
Notice that this value will be one side of the rectangle, while the larger base (that is, 2x) will be the other side of the rectangle. We ultimately want to solve for 2x*h.
So if we have:
((x + 2x)/2) * h = 30
That is, (3xh)/2 = 30, which simplifies to xh = 20.
And therefore we can determine that 2xh = 2*20 = 40.
The answer is A.
The area of a rectangle is, of course, base*height.
The quadrilateral that would form as QRPT is a trapezoid because it has two parallel sides and two non-parallel sides. The area of a trapezoid is this:
((base_1 + base_2)/2) * height
Now, if we look at the trapezoid, using p as the midpoint of side RS, we see that base_1 will be exactly half of base_2. Let's call base_1 = x, which makes base_2 = 2x. For good measure, let's call the height = h.
Notice that this value will be one side of the rectangle, while the larger base (that is, 2x) will be the other side of the rectangle. We ultimately want to solve for 2x*h.
So if we have:
((x + 2x)/2) * h = 30
That is, (3xh)/2 = 30, which simplifies to xh = 20.
And therefore we can determine that 2xh = 2*20 = 40.
The answer is A.
gmatclubot
Re: In rectangle QRST, point P is the midpoint of side RS. If the area of [#permalink]
20 Jun 2022, 07:50
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