Answer:
The answer is option 1.
Explanation:
First, you have to find the value of y. In order to find y, you have to use the area of rectangle as the question has given the area's value and the expressions for length and width :
Let area be 84 cm²,
Let length be (y+5) cm,
Let width be y cm,
Area = length×width
84 = y(y+5)
84 = y² + 5y
Next, you have to solve this equation by factorization :
y² + 5y = 84
y² + 5y - 84 = 0
y² + 12y - 7y - 84 = 0
y(y+12) - 7(y+12) = 0
(y-7)(y+12) = 0
y - 7 = 0
y = 7 cm
y + 12 = 0
y = -12 cm (rejected)
Lastly, you have to find the perimeter of rectangle using the formula, P = 2l + 2w where l represents length and w is width.
P = 2(y+5) + 2(y)
Let y = 7 cm,
P = 2(7+5) + 2(7)
= 2(12) + 14
= 24 + 14
= 38 cm