What is the factorization??
1 answer:
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Explanation:
a. The line joining the midpoints of the parallel bases is perpendicular to both of them. It is the line of symmetry for the trapezoid. This means the angles and sides on one side of that line of symmetry are congruent to the corresponding angles and sides on the other side of the line. The diagonals are the same length.
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b. We observe that adjacent pairs of points have the same x-coordinate, so are on vertical lines, which have undefined slope. KN is a segment of the line x=1; LM is a segment of the line x=3. If the trapezoid is isosceles, the midpoints of these segments will be on a horizontal line. The midpoint of KN is at y=(3-2)/2 = 1/2. The midpoint of LM is at y=(1+0)/2 = 1/2. These points are on the same horizontal line, so the trapezoid <em>is isosceles</em>.
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c. We observed in part (b) that the parallel sides are KN and LM. The coordinate difference between K and L is (1, 3) -(3, 1) = (-2, 2). That is, segment KL is the hypotenuse of an isosceles right triangle with side lengths 2, so the lengths of KL and MN are both 2√2.
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For part (c), we used the shortcut that the hypotenuse of an isosceles right triangle is √2 times the leg length.
Answer:
6m
Step-by-step explanation:
the side of first square = 3 m
area of first square = 3^2= 9 m^2
let the side of second square = x m
since diagonal of first square = x m as per the question
in a square each angle is 90 degree
therefore by applying pythagorus theorem ,
diagonal ^2 = side^2 + side ^2
diagonal^2 = 3^2+3^2=9+9
DIAGONAL= square root of 18
diagonal= 3 m = side of second square
therefore in second square ,
one angle is 90 degree , therefore by applying pythagorue theorem
diaqonal^2 = side ^2 + side ^2 = (3)^2 + ( 3
)^2
diagonal ^2 = 18 + 18
diagonal = square root of 36
therefore diagonal of second square is 6m
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