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inside a large Square three small
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squares were placed as shown in the
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figure the areas of two small squares
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16 find the area of the third small
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square if the area of the remaining part
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of the large square is equal to
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58 as usual before watching press pause
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and try to solve the problem according
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to the given formula the area of a
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square is equal to the square of its
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side which means the side of the square
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will be equal to the square root of its
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area therefore the side of the first
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square whose area is equal to 16 will be
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equal to the square OT of 16 which is
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equal to 4 the side of the second square
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whose area is equal to 4 will be equal
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to the square < TK of 4 which is equal
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to 2 let's denote the side of the small
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square whose area we need to find as X
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then its area will be equal to x^2 this
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is the value we need to find let's try
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to do this using the area of the large
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Square on one hand the area of the large
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square is equal to the square sare of
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its side 4 + x + 2 we get x + 6 and we
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Square it on the other hand the area of
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the large square is equal to the sum of
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the areas of all its parts that is it
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will be equal to the sum of the areas of
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the small squares plus the area of the
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remaining part of the large square that
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is + 58 now from the resulting equation
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let's try to find the side of the square
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we need to do this first expand the
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square of the sum we get x^2 + 12 x + 36
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and on the right side of the equation
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after combining like terms we get x^2 +
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78 we subtract X squar from both sides
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and move 36 to the right side we get 12x
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= the difference 78 - 36 from which 12x
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= 42 therefore X will be equal to 42 /
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12 simplifying we get 7 halves or in
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decimal form this will be 3.5 now we can
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find the area we need which is equal to
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x^2 we get 7^ SAR which equal 49/4 that
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is 12 12 and 1/4 or in decimal form this
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will be 12.25 the answer is that the
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area of the third small square in the
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figure is 12.25 square units the problem
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is solved if the solution is clear give
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it a like and be sure to leave a few
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words in the comments for this video
