The ratio of length to width of a rectangular garden is 6:7. If the perimeter of the rectangle is 78 cm.What is the area of the garden?
A: 274
B: 378
C: 352
D: 380
The perimeter (P) of a rectangle is given by the formula:
P=2 × (length + width)
In this case, the perimeter is given as 78 cm. Therefore:
78 = 2 × ( 6x + 7x )
Combine like terms:
78 = 2 × 13x
Divide both sides by 2:
39 = 13x
Solve for x:
X = 39/13 = 3
Now that we have the value of x, we can find the length and width of the rectangle:
Length = 6x = 6 × 3 = 18cm
Width = 7x = 7 × 3 = 21cm
Now, we can find the area (A) of the rectangle using the formula:
A = length × width
A = 18cm × 21cm
A = 378cm2
Therefore, the area of the rectangular garden is 378cm2.
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