Answer :
Final answer:
To find the perimeter of a rectangle with a given area where the length is 5cm longer than the width, we first solve for the width using a quadratic equation, then calculate length, and use the perimeter formula. The perimeter of the given rectangle is 54cm.
Explanation:
The question states that the length of a rectangle is 5cm longer than its width and that its area is 176cm2. To find the perimeter, we need to determine the rectangle's dimensions first.
Let's assume the width of the rectangle is x cm. Then, the length will be (x + 5) cm. According to the area given, the product of the width and length is 176 cm2, so we have:
x imes (x + 5) = 176
x2 + 5x - 176 = 0
This is a quadratic equation that can be solved using factorization, yielding two potential solutions for x. We find that x = 11 and x = -16. Since a negative width is not possible physically, the width must be 11 cm, making the length 11 + 5 = 16 cm.
The perimeter (P) of a rectangle is given by P = 2l + 2w, where l is the length and w is the width. Substituting the found dimensions:
P = 2(16) + 2(11) = 32 + 22 = 54 cm
So, the perimeter of the rectangle is 54 cm.
