1998 AHSME Problem 10

Geometry Level 1

A large square is divided into a small square surrounded by four congruent rectangles as shown. The perimter of each of the congruent rectangles is 14. What is the area of the large square?

64 49 121 100

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4 solutions

Rifath Rahman
Jul 3, 2014

p=2(l+b)=14 so l+b=7 now from the figure if we can see the bigger square's side can be expressed as the half of the perimeter so the area of the square is 7^2=49

Mikhaella Layos
May 27, 2014

let a a and b b be the measurements of 2 non congruent sides of the rectangle. Then, P = 2 ( a + b ) = 14 P=2(a+b)=14 a + b = 7 a+b=7

From the figure above, the measure of a side of the bigger square can be expressed as a + b a+b ,which is equal to 7. Hence, the area of the bigger square is ( a + b ) 2 = 7 2 = 49 (a+b)^{2}=7^{2}=\boxed{49}

since perimeter of each rectangle is 2(length breadth)=14, by solving this we get length (l b=7 )of large square as 7 and area is 7*7=49

Krishna Garg
Apr 12, 2014

Each rectangle will have length 5 and width 2 cm. So total side vlength is 7 Cm so area of square is 7X7 =49 Ans K.K.GARG,India

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