two figures are shown. figure a is a square and figure b is a rectangle. the perimeter of figure a is equal to perimeter of figure
__3x-2_____
| |
| |
3x-2| | 3x-2
|___________|
3x-2
____________________
| |
| |
| | x-2
|___________________|
2x+5
What is the value of x?
a. 3/7
b. 7/3
c. 8
d. 14
My answer is in-between b and d may you help me out?
so, did you actually use the value(s) and see whether they worked? Being able to check your answer is just as important as getting it in the first place!
if the perimeters are equal, then
4(3x-2) = 2(x-2 + 2x+5)
4(3x-2) = 2(3x+3)
2(3x-2) = 3x+3
6x-4 = 3x+3
3x = 7
x = 7/3
To find the value of x, we can equate the perimeters of the square and rectangle.
Perimeter of a square = 4 * side length
Perimeter of a rectangle = 2 * (length + width)
From the given figure, we can see that the side length of the square is 3x-2, and the dimensions of the rectangle are (2x+5) by (x-2).
Therefore, we can set up the equation:
4 * (3x-2) = 2 * [(2x+5) + (x-2)]
Now let's solve for x:
4 * (3x-2) = 2 * [2x + 5 + x - 2] [distributing the 2]
12x - 8 = 2 * (3x + 3) [simplifying]
12x - 8 = 6x + 6 [distributing the 2]
12x - 6x = 8 + 6 [combining like terms]
6x = 14 [simplifying]
x = 14/6 [dividing both sides by 6]
Simplifying the fraction, we get:
x = 7/3
So, the value of x is 7/3, which corresponds to option b.
Therefore, option b. 7/3 is the correct answer.
To find the value of x, we can equate the perimeters of the two figures.
The perimeter of a square is calculated by adding the lengths of all four sides. Since figure A is a square with side length 3x - 2, its perimeter is equal to 4 times the side length:
Perimeter of figure A = 4(3x - 2) = 12x - 8
The perimeter of a rectangle is calculated by adding the lengths of two adjacent sides and multiplying it by 2. In figure B, the length is 2x + 5 and the width is x - 2. So the perimeter of figure B can be calculated as:
Perimeter of figure B = 2(2x + 5 + x - 2) = 2(3x + 3) = 6x + 6
Now, we can set the perimeters equal to each other and solve for x:
12x - 8 = 6x + 6
First, let's simplify the equation by combining like terms:
12x - 6x = 6 + 8
6x = 14
To isolate x, divide both sides of the equation by 6:
x = 14/6 = 7/3
Therefore, the value of x is 7/3.
So, the correct option is b. 7/3.