Answer:
L = 3.4 m
w = 0.6 m
Step-by-step explanation:
Let L be the length of the rectangle
w be the width
P be the perimeter
A be the area
…………………………………………
FORMULA :
P = 2×(L + w)
A = L × w
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P = 8 ⇔ 2×(L + w) = 8 ⇔ L + w = 4 ⇔ L = 4 - w
A = 2 ⇔ L × w = 2 ⇔ (4 - w) × w = 2 ⇔ w² - 4w + 2 = 0
we have to solve this equation in order to find w :
w² - 4w + 2 = 0
Then
(w - 2)² - 4 + 2 = 0
Then
(w - 2)² = 2
Then
w - 2 = ±√2
Then
w = 2 ± √2
……………………
If w = 2 + √2 then L = 4 - w = 4 - (2 + √2) = 2 - √2 absurd because L > w.
If w = 2 - √2 then L = 4 - w = 4 - (2 - √2) = 2 + √2 .
Conclusion :
• L = 2 + √2 = 3.414213562373
• w = 2 - √2 = 0.585786437627
