To determine which of the rectangles has a different area, the areas of the four rectangles must be calculated. The rectangle with a different area is rectangle b
The dimension of the 4 rectangles are:
a. length: 4x and width: 4
b. length: 11 and width: x
c. length: 2 and width: 8x
d. length: 16x and width: 1
The area of a rectangle is:
<u>Rectangle (a)</u>
<u>Rectangle (b)</u>
<u>Rectangle (c)</u>
<u>Rectangle (d)</u>
Rectangles (a), (c) and (d) have the same area (i.e. 16x) while rectangle (b) has 11x as its area.
Hence, the rectangle with a different area is rectangle (b).
Read more about areas of rectangles at:
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Step-by-step explanation:
Starting from the upper left in the clockwise direction:
congruent: no
similar: no
upper right side:
congruent: yes
similar: yes
lower right side:
congruent: no
similar: yes
lower left side:
congruent: yes
similar: yes
~ Simplifying
-4x + -4 = -7(x + 4)
~ Reorder the terms:
-4 + -4x = -7(x + 4)
~ Reorder the terms:
-4 + -4x = -7(4 + x)
-4 + -4x = (4 * -7 + x * -7)
-4 + -4x = (-28 + -7x)
~ Solving
-4 + -4x = -28 + -7x
~ Solving for variable 'x'.
~ Move all terms containing x to the left, all other terms to the right.
~ Add '7x' to each side of the equation.
-4 + -4x + 7x = -28 + -7x + 7x
~ Combine like terms: -4x + 7x = 3x
-4 + 3x = -28 + -7x + 7x
~ Combine like terms: -7x + 7x = 0
-4 + 3x = -28 + 0
-4 + 3x = -28
~ Add '4' to each side of the equation.
-4 + 4 + 3x = -28 + 4
~ Combine like terms: -4 + 4 = 0
0 + 3x = -28 + 4
3x = -28 + 4
~ Combine like terms: -28 + 4 = -24
3x = -24
~ Divide each side by '3'.
x = -8
~ Simplifying
x = -8
For this case we have the following system of equations:
From the first equation we clear "x":
We substitute in the second equation:
We apply distributive property:
We add similar terms:
We add 65 to both sides:
We divide between 22 on both sides:
We look for the value of the variable "x":
Thus, the solution of the system is:
ANswer:
