The perimeter of the rectangle below is 208 units. Find the length of side AB .
Write your answer without variables.
DA 4x+3 AB 5x+2 BC unknown
no figure to see. But you know that AB is the same as CD.
and 2(AB+BC) = 208
Well, it seems we have a mystery on our hands. Let's see if we can solve it!
To find the perimeter of a rectangle, you add up the lengths of all its sides. In this case, we know that the perimeter is 208 units. So, let's set up an equation:
AB + BC + CD + DA = 208
But wait! We're looking for the length of side AB specifically. So let's focus on that:
AB = 208 - (BC + CD + DA)
Now, we don't know the values of BC, CD, and DA, but we do know that DA is 4x + 3 and AB is 5x + 2. So we can substitute those expressions into our equation:
5x + 2 = 208 - (BC + CD + (4x + 3))
Alright, let's simplify this expression:
5x + 2 = 208 - BC - CD - 4x - 3
Hmm, things are getting tricky. Let's gather like terms:
9x - BC - CD = 203
We're getting closer! Now, we need more information about BC and CD to solve this equation. Do you have any additional measurements or clues to help us out?
To find the length of side AB, we need to use the formula for the perimeter of a rectangle, which is P = 2(l + w), where P is the perimeter and l and w are the length and width of the rectangle, respectively.
In this case, we know that the perimeter is 208 units, so we can write the equation as:
208 = 2(AB + BC)
We are given that DA = 4x + 3 and AB = 5x + 2, so we can substitute these values into the equation:
208 = 2((5x + 2) + BC)
Now, let's solve for BC.
Distribute the 2 on the right side of the equation:
208 = 10x + 4 + 2BC
Subtract 4 from both sides of the equation to isolate the terms with BC:
204 = 10x + 2BC
Now, divide both sides of the equation by 2 to solve for BC:
102 = 5x + BC
Finally, rewrite the equation with x and BC on the left side:
BC = 102 - 5x
Therefore, the length of side AB (AB = 5x + 2) is 5x + 2 units.
To find the length of side AB, we need to use the given information about the perimeter of the rectangle.
The perimeter of a rectangle is the sum of the lengths of all its sides. In this case, we are given that the perimeter is 208 units.
The perimeter of a rectangle can be calculated by adding the lengths of the opposite sides together. In this case, the opposite sides are AB and DA, and they have lengths of (5x+2) and (4x+3) units, respectively.
So, the equation to find the perimeter is:
Perimeter = AB + DA + AB + DA
208 = (5x+2) + (4x+3) + (5x+2) + (4x+3)
Now, let's simplify the equation:
208 = 5x + 2 + 4x + 3 + 5x + 2 + 4x + 3
Combine like terms:
208 = 18x + 10
Now, let's isolate x by moving the constant term to the other side:
208 - 10 = 18x
198 = 18x
Divide both sides by 18 to solve for x:
x = 198 / 18
x = 11
Now that we know the value of x, we can substitute it back into the equation to find the length of side AB:
AB = 5x + 2
AB = 5(11) + 2
AB = 55 + 2
AB = 57
Therefore, the length of side AB is 57 units.