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xxMikexx [17]
3 years ago
15

Question 28 of 42

Mathematics
1 answer:
lina2011 [118]3 years ago
5 0

Answer with explanation:

Properties of Rectangle

1. Opposite sides are equal and parallel.

2. Diagonals are equal and bisect each other.

3. Adjacent Sides are Perpendicular to each other.

→If two lines are parallel their slopes are equal and if two Lines are perpendicular, their product of slopes is -1.

→A Rectangle is a Quadrilateral also.

→Adjacent sides are perpendicular ,so , their slopes can't be equal.Product of their slopes should be equal to ,-1.

⇒Slope of AB × Slope of BC = -1

⇒Also, Slope of AB × Slope of BC = -1

Slope of AB × Slope of AD = -1

⇒ Slope of AD × Slope of CD = -1

Slope of CB × Slope of CD = -1

Option B And Option C

are statement which proves that polygon ABCD is not a rectangle.

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Given that segment AB is tangent to the circle shown in the diagram centered at point C, determine the value of x
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Step-by-step explanation:

This problem can be solved by applying Pythagoras theorem, since the segment AB is tangent to the circle(meaning that the point A is at 90 degree to the circle)

According to Pythagoras theorem "It states that the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides".

given (as seen from the diagram)

x, hypotenuse= ?

opposite= 12

adjacent= 35

Applying Pythagoras theorem

hyp^2= opp^2+adj^2\\\\hpy=\sqrt{opp^2+adj^2}

Substituting our given data and solving for hpy we have

hyp=\sqrt{12^2+35^2} \\\\hyp=\sqrt{144+1225}\\\\hyp=\sqrt{1369}\\\\hyp= 37

hence x= 37

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