Question

The dimensions of a rectangle are y and y^2 + 1, and the perimeter of the rectangle is 14 units. What are the dimensions of the rectangle?

a) y = 2, y^2 + 1 = 3
b) y = 3, y^2 + 1 = 10
c) y = 4, y^2 + 1 = 17
d) y = 5, y^2 + 1 = 26

Answer 1

The dimensions of the rectangle are y = 2 and y^2 + 1 = 3.

Step-by-step explanation:

To find the dimensions of the rectangle, we can set up an equation using the perimeter formula. The formula for the perimeter of a rectangle is P = 2(y + y^2 + 1), where y represents the length and y^2 + 1 represents the width. We are given that the perimeter is 14 units, so we can write the equation as follows:

14 = 2(y + y^2 + 1)

Simplifying the equation, we get: 7 = y + y^2 + 1

Combining like terms, we have: y^2 + y - 6 = 0

Factoring the quadratic equation, we find (y + 3)(y - 2) = 0

Setting each factor equal to zero, we get y + 3 = 0 and y - 2 = 0

Solving for y, we find y = -3 and y = 2

Since the dimensions cannot be negative, the dimensions of the rectangle are y = 2 and y^2 + 1 = 3.