Question

A rectangle has a length of (2x + 3) cm and a width of (x + 5) cm. The rectangle has a perimeter of 43 cm. Find the value of x.

Answer 1

To find the value of x in the given rectangle with a perimeter of 43 cm, we use the formula for perimeter and solve the resulting equation. The value of x is approximately 4.5 cm.

Step-by-step explanation:

To find the value of x, we need to use the fact that the perimeter of the rectangle is 43 cm. The formula for the perimeter of a rectangle is P = 2(L + W), where P is the perimeter, L is the length, and W is the width. In this case, we can substitute the given length and width into the formula and solve for x.

43 = 2((2x + 3) + (x + 5))

Now, let's simplify the equation.

43 = 2(3x + 8)

43 = 6x + 16

Subtracting 16 from both sides gives us:

27 = 6x

Finally, divide both sides by 6 to solve for x:

x = 27/6

Therefore, the value of x is approximately 4.5 cm.