Answer: 15cm and 5cm
Step-by-step explanation:
A rectangle's area is the product of the length and width
Given length x and width y, 2x+2y = 40 and x*y = 75.
Verifying my answer:
2(15)+2(5) = 40
30+10 = 40
40 = 40
15*5 = 75
75= 75
This is a week late so I hope this helped.
The length and the width of the rectangle are 15cm and 5cm respectively
The given parameters are:
Area (A) = 75
Perimeter (P) = 40
The area of a rectangle is LW, while the perimeter is 2(L + W)
So, we have:
LW = 75
2(L + W) = 40
Divide by 2
L + W = 20
Make L the subject
L = 20 - W
Substitute L = 20 - W in LW = 75
(20 - W)W = 75
Expand
20W - W^2 = 75
Rewrite as:
W^2 - 20W + 75 = 0
Expand
W^2 - 15W - 5W + 75 = 0
Factorize
(W - 15)(W -5) = 0
Split
W - 15 = 0 or W - 5 = 0
Solve for W
W = 15 or W = 5
Recall that:
L= 20 - W
So, we have
L = 20 - 15 or L = 20 - 5
This gives
L = 5 or L = 15
Hence, the length and the width of the rectangle are 15cm and 5cm respectively
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