Answer:
x = 7
Explanation:
Step 1: Find measures of other two sides of first rectangle:
- The figure is a rectangle and rectangles have two pairs of equal sides.
Thus:
- the side opposite the (2x - 5) ft side is also (2x - 5) ft long,
- and the side opposite the 3 ft side is also 3 ft long.
Step 2: Find measures of other two sides of second rectangle:
- the side opposite the 5 ft side is also 5 ft long,
- and the side opposite the x ft long is also x ft.
Step 3: Find perimeter of first and second rectangle:
The formula for perimeter of a rectangle is given by:
P = 2l + 2w, where
- P is the perimeter,
- l is the length,
- and w is the width.
Perimeter of first rectangle:
- In the first rectangle, the length is (2x - 5) ft and the width is 3 ft.
Now, we can substitute these values for l and w in perimeter formula to find the perimeter of the first rectangle:
P = 2(2x - 5) + 2(3)
P = 4x - 10 + 6
P = 4x - 4
Thus, the perimeter of the first rectangle is (4x - 4) ft
Perimeter of the second rectangle:
- In the second rectangle, the length is 5 ft and the width is x ft.
Now, we can substitute these values in for l and w in the perimeter formula:
P = 2(5) + 2x
P = 10 + 2x
Thus, the perimeter of the second rectangle is (10 + 2x) ft.
Step 4: Set the two perimeters equal to each to find x:
Setting the perimeters of the two rectangles equal to each other will allow us to find the value for x that would make the two perimeters equal each other:
4x - 4 = 10 + 2x
4x = 14 + 2x
2x = 14
x = 7
Thus, x = 7
Optional Step 5: Check validity of answer by plugging in 7 for x in both perimeter equations and seeing if we get the same answer for both:
Plugging in 7 for x in perimeter equation of first rectangle:
P = 4(7) - 4
P = 28 - 4
P = 24 ft
Plugging in 7 for x in perimeter equation of second rectangle:
P = 10 + 2(7)
P = 10 + 14
p = 24 FT
Thus, x = 7 is the correct answer.