John was told that the rectangle had a side length of

Question

John was told that the rectangle had a side length of 
5
x
+
20
 
f
t
5x+20 ft and the other side length was 
2
x
+
23.
2x+23.  If the perimeter of the rectangle was 
208.5
 
f
t
208.5 ft then what is the value of 
x
x

GPT-4o mini · Answer

To find the value of $ x $ in the rectangle's side lengths, we first need to use the formula for the perimeter of a rectangle. The perimeter $ P $ of a rectangle is given by: $$ P = 2 \times (\text{length} + \text{width}) $$ Given the side lengths: - Length $ = 5x + 20 $ ft - Width $ = 2x + 23 $ ft We can plug these into the perimeter formula: $$ 208.5 = 2 \times ((5x + 20) + (2x + 23)) $$ Simplifying inside the parentheses: $$ 208.5 = 2 \times (5x + 20 + 2x + 23) $$ $$ 208.5 = 2 \times (7x + 43) $$ Next, we'll distribute the 2: $$ 208.5 = 14x + 86 $$ Now, we solve for $ x $ by isolating $ x $. First, subtract 86 from both sides: $$ 208.5 - 86 = 14x $$ $$ 122.5 = 14x $$ Next, divide by 14: $$ x = \frac{122.5}{14} $$ $$ x = 8.75 $$ Thus, the value of $ x $ is $ \boxed{8.75} $.

Answer

John found that the perimeter of a square is 4 x + 21 4x+21 f t ft . If the perimeter's length is 100 f t 100 ft what is the value of x x ?

GPT-4o mini · Answer

The perimeter $ P $ of a square is given by the formula: $$ P = 4 \times \text{side length} $$ In this case, we know that the perimeter is represented as $ 4x + 21 $ ft, and it's given that $ P = 100 $ ft. Therefore, we can set up the equation: $$ 4x + 21 = 100 $$ Now, we'll solve for $ x $. First, subtract 21 from both sides: $$ 4x + 21 - 21 = 100 - 21 $$ $$ 4x = 79 $$ Next, divide both sides by 4: $$ x = \frac{79}{4} $$ $$ x = 19.75 $$ Thus, the value of $ x $ is $ \boxed{19.75} $.