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in a right triangle three squares are
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inscribed the areas of two of them are
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four and 9 find the area of the third
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Square as usual pause the video before
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watching and try to solve the problem
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the area of a square is equal to the
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square of its side this means that the
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side of the square is equal to the
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square root of its area let's find the
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side of the small square and denote it
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as A1 it will be equal to the square <
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TK of 4 which is 2 next let's find the
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side of the medium square and denote it
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as as A2 it will be equal to the square
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< TK of 9 which is 3 the difference
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between the sides of the two squares
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will then be equal to 3 - 2 which equals
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1 all the angles of the squares are
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right angles therefore the lines on
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which the sides of the two squares lie
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will be perpendicular to the third line
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if two lines are perpendicular to a
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third line they are parallel when two
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parallel lines are intersected by a
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transversal corresponding angles are
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equal this means the two right triangles
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will be similar by the acute angle in
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similar triangles corresponding sides
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are proportional in this case we will
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use the proportionality of corresponding
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legs let the unknown leg be denoted as X
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the ratio of one pair of legs x: 1 will
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be equal to the ratio of the second pair
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of legs 3 / 2 dividing 3 by 2 gives 1
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and 1/2 thus the side of the third
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Square which was equal to the sum of x +
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3 will be 4 and 1/2 therefore its area
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will be equal to 4 1/2 s which results
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in 20.25 we write the answer the area of
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the square is 20.25 square units the
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solved if you understood the solution
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give it a like leave a comment and don't
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