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alina1380 [7]
3 years ago
13

Properties of rectangle

Mathematics
2 answers:
Alexandra [31]3 years ago
8 0

4. y = 5

5. DB = 27

6. AC = 18

7. m<ABD = 53

Nat2105 [25]3 years ago
6 0

For this case we have:

Question 1:

BC = 24\\AD = 5y-1

By definition, one of the properties of the rectangle states that:

The opposite sides of a rectangle have the same length, that is, they are equal, then:

BC = AD

So:

24 = 5y-1

Clearing "y" we have:

24 + 1 = 5y\\25 = 5y\\y = \frac {25} {5}\\y = 5

Thus, the value of "y" is 5.

Answer:

y = 5

Question 2:

AC = 2x + 13\\DB = 4x-1

By definition, one of the properties of the rectangles states that:

 The diagonals of a rectangle have the same lengths, that is:

AC = DB\\2x + 13 = 4x-1

We clear the value of "x":

13 + 1 = 4x-2x\\14 = 2x\\x = \frac {14} {2}\\x = 7

We must find DB:

DB = 4x-1 \\DB = 4 (7) -1\\DB = 28-1\\DB = 27

ANswer:

DB = 27

Question 3:

AE = 3x + 3\\EC = 5x-15

By definition, one of the properties of the rectangles states that:

The diagonals of a rectangle intersect and at the point of intersection they are divided in half, that is:

AE = EC\\3x + 3 = 5x-15

Clearing the value of "x" we have:

3 + 15 = 5x-3x\\18 = 2x\\x = \frac {18} {2}\\x = 9

We know that:

AC = AE + EC\\AC = 3x + 3 + 5x-15\\AC = 8x-12\\AC = 8 (9) -12\\AC = 60

ANswer:

AC = 60

Question 4:

m

By definition, one of the properties of the rectangles states that:

The 4 angles of the rectangles are straight. From there it turns out that:

m

We clear the value of "x":

7x-4x = 5 + 31\\3x = 36\\x = \frac {36} {3}\\x = 12

So:

m

Answer:

m

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