Question

ASAP!!!!!!!!! PLS!!!!!

Answer 1

`\huge\boxed{\text{6 by 10 inches}}`

Explanation:

In order to solve for this, we can make two equations, where a is the length of the first side and b is the length of the second side.

• 
  `ab=60` (Area)
• 
  `2a+2b=32` (Perimeter)

We can now solve this systems of equations by using substitution.

Let's change the equation
`ab=60` into the form
`a= mb+c`.

We can divide both sides by b.

`a = (60)/(b)`

We can now plug
`(60)/(b)` in as a into
`2a+2b=32`.

`2((60)/(b)) + 2b = 32`

Let's simplify this equation:

• 
  `(120)/(b) + 2b = 32`
• 
  `2b^2 + 120 = 32b`
• 
  `2b^2 - 32b + 120 = 0`
• 
  `b^2 - 16b + 60 = 0`
• 
  `-10 \cdot -6 = 60\\-10 + -6 = -16` (Quadratic factoring,
  `x_1 \cdot x_2=c, x_1 + x_2 = b`)
• 
  `(b-10)(b+6)`
• 
  `b = 10\ \text{or}\ 6`

Now, since we have both roots of this quadratic, we know that the two sides will be 10 and 6 inches long.

Hope this helped!