Given rectangle ABCD below,
a. Find the measure of the angles labeled below.
b. If the length of AB=3x–21, DC=34, BC=4y+32, and AD=62, find the values of x and y.
c. Find the perimeter and area of rectangle ABCD.

(x, y) = (18 1/3, 7 1/2)perimeter = 192area = 2108

Step-by-step explanation:

a) no angles are described or shown

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b) Opposite sides are the same length, so we have ...

  3x -21 = 34

  3x = 55 . . . . . . . add 21

  x = 55/3 = 18 1/3 . . . . . divide by 3

and

  4y +32 = 62

  4y = 30 . . . . . . . . subtract 32

  y = 15/2 = 7 1/2 . . . . divide by 4

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c) The perimeter is the sum of the side lengths, so is ...

  P = 2(L+W) = 2(62 +34) = 192 . . . units

The area is the product of adjacent side lengths, so is ...

  A = LW = 62·34 = 2108 . . . square units

What we're dealing with is the Distributive Property. This allows any number/variable outside of a parenthesis to multiply by all numbers/variables inside of the parenthesis.

For example:

2(1 + 3)
2(1) + 2(3)
2 + 6
8.

Now that we've broken down what we're dealing with, let's try to solve.

-3(b + 19) = -12
-3(b) + -3(19) = -12
-3b -57 = -12
Add 57 to both sides to get -3b by itself.
-57 + 57 = 0
-12 + 57 = 45

-3b = 45
Divide both sides by -3 to solve for b.

-3b / -3 = b
45 / -3 = -15

b = -15

I hope this helps! PM me if you need help understanding.