Final answer:
To triple the area of his 10x12 feet deck, Samir must increase each dimension by 8 feet. The solution involves setting up and solving a quadratic equation based on the desired area.
Step-by-step explanation:
Samir has a deck measuring 10 feet by 12 feet and wants to increase each dimension equally so that the area is tripled.
To solve this, we can set up an equation where the side lengths after the increase are x feet longer than the original dimensions.
The original area is 120 square feet (10 ft × 12 ft), and tripling this gives us an area of 360 square feet.
Let's denote the new length of the deck as (10 + x) feet and the new width as (12 + x) feet. To find the increased length x, we can set up the equation:
(10 + x)(12 + x) = 360
We expand this to:
120 + 22x + x² = 360
Subtract 360 from both sides to set the equation to zero:
x² + 22x - 240 = 0
Now we use the quadratic formula, a² + bx + c = 0, to solve for x.
The factors of the quadratic equation we end up with are x = 8 and x = -30.
Since a negative increase isn't logical in this context, we know Samir needs to increase each dimension by 8 feet to triple the area of his deck.