Squares A, B, C and D are placed as shown in the diagram above. Two sm

Question

https://gmatclub.com/forum/download/file.php?id=55382 Squares A, B, C and D are placed as shown in the diagram above. Two smaller squares B and C have side length of 1. What is the area of blue triangle? A. 2 B. 3 C. 2\sqrt{2} D. 2\sqrt{3} E. 4 Project PS Butler Subscribe to get Daily Email - Click Here | Subscribe via RSS - RSS Are You Up For the Challenge: 700 Level Questions 2020-06-17_1424.png

ScottTargetTestPrep · Accepted Answer

Solution: We are given the side lengths of squares B and C are both 1. Therefore, the side length of square A is 2. However, we are not given and we can’t determine the side length of square D. So let’s let the side length of square D be x. In addition, we will have a rectangle that encloses the 4 squares (see diagram below). solution5.png We see that if we subtract the sum of the areas of the two triangles above the shaded triangle and the trapezoid below it from the area of the rectangle that encloses the squares, then we have the area of the shaded triangle. Area of the rectangle = 3(x + 2) Area of the triangle above the shaded triangle to the right = ½(1)(1) = 1/2 Area of the triangle above the shaded triangle to the left = ½(3 - x)(x + 1) = ½(3 + 2x - x^2) Area of the trapezoid below the shaded triangle = ½(x + 2)(x + 2) = ½(x^2 + 4x + 4) Therefore, the area of the shaded triangle is: Area = 3(x + 2) - Area = 3x + 6 - Area = 3x + 6 - Area = 3x + 6 - 4 - 3x = 2 Answer: A

GMATinsight · Answer

Please check the explanation as attched

Answer: Option A

Please check the video for the step-by-step solution.

https://www.youtube.com/watch?v=-oDfHzfajWI

yashikaaggarwal · Answer

Diagonal of square C 
WV = √1+1 
WV = √2
Square A side = Square B + Square C Sides = 2
draw diagonal VS and connect dot WS
A triangle drawn from same base has equal area.
Triangle UVW = Triangle VWS
VS is Diagonal of square A
VS^2 = VR^2+RS^2
VS^2 = 2^2+2^2
VS^2 = 4+4
VS^2 = 8
VS = 2√2
Therefore Area of triangle WVS
Area of SVW = 1/2*√2*2√2
Area of SVW = 2 = Area of UVW

Answer is A

IanStewart · Answer

We're told nothing about square D, so if this question has a unique answer (which it must; otherwise it couldn't be asked in this way), that answer must not depend on the size of square D. So we can make it any size we want. One way to do the problem is to make D a 1x1 square. Then you could draw another square overtop of D which is also 1x1, and the squares on the left of the diagram become identical to those on the top of the diagram. It's easy from there to see that the blue triangle becomes a right triangle, with the right angle at the top, and its two legs have lengths √2 and 2√2 (one leg is the diagonal of a 1x1 square, the other two diagonals of 1x1 squares), so its area is 2.

mSKR · Answer

why blue area should have same area as newly drawn triangle?

HoneyLemon · Answer

GMATinsight  I could not understand the logic behind how this blue Triangle as same as newly formed triangle .

May you please help on the same.

GMATinsight · Answer

DasAshishAshutosh Draw diagonal of square D This diagonal is parallel to diagonal of square B when height is distance between two parallel lines, The area of two triangles with same base will be same. So base and height of given blue triangle and triangle that I have drawn will be same. Hope this help!

HoneyLemon · Answer

Yes . I got the same now. Thank you  GMATinsight  ..

mSKR · Answer

I know that if base is same then inscribed angles subtended by same arc are equal

i am sorry, i still didn't get the relationship of parallel diagonal , the diagonals B and D are not of same length.

is there any name for such theorem?

GMATinsight · Answer

Two triangles drawn between two parallel lines which have the same base will also have same height (distance between parallel sides and hence their Areas will be same

bumpbot · Answer

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Squares A, B, C and D are placed as shown in the diagram above. Two sm

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