Question

The length of a rectangle is (2x + 4) and the width is (3x - 2) with a perimeter of 104cm.

Write and solve an equation to determine the length and width of the rectangle. Explain how you
determine your answer.

Answer 1

length = 24 cm

width = 28 cm

Explanation:

Since p = 2(l + w), we can form an equation and solve for x to find the missing sides with our algebraic expressions given that our length [l] is (2x + 4), our width [w] is (3x - 2), and our perimeter [p] is 104 cm.

p = 2(l + w) → [104] = 2([2x + 4] + [3x - 2]) →

104 = 2(5x + 2) → 104 = 10x + 4 →

100 = 10x → 10 = x → x = 10

Now that we have the value of x, we can substitute this into our given expressions of the length and width to find the actual length in centimeters.

So, x = 10 → l = (2x + 4) → l = (2[10] + 4) →

l = 24.

And, x = 10 → w = (3x - 2) → l = (3[10] - 2) →

w = 28.

Also we can prove these answers are correct because:

p = 2(l + w) → [104] = 2([24 + 28]) →

104 = 2(52) → 104 = 104.

Answer 2

The length of a rectangle is (2x + 4) and the width is (3x - 2) with a perimeter of 104cm.

Write and solve an equation to determine the length and width of the rectangle. Explain how you

determine your answer.