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ladnerhailey16
21.12.2020 •
Mathematics
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.
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Ответ:
length = 24 cm
width = 28 cm
Step-by-step 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.
Ответ: