here is a question about measurements.

Question

Jarom is working for a landscaping company and is responsible for building the stone border around a rectangular pond. The pond measures 6 meters by 15 meters. The manager told Jarom that the budget only allowed enough stone for 46 square meters and to make the stone border as wide as possible. How wide can the border be?

Answer 1

Let the border be width x. Then the area of the border will be 2(6x) + 2(15x) + 4x² = 46 (Draw the diagram if this isn't clear)

Find x for 4x² + 42x -46 = 0 or x² +13x - 14 = 0

This is factorable or you can use the quadratic formula.

Answer 2

Hey!

For starters we know that A=lw. This means that the area of the pond is 90 m². We're also given that the border is 46 m², for a total area of 136 m².

We're looking for the width within the total area! Since we don't know the width or the length for either one for the border, but we do know the area's length and width for the pool, let's define our variables like so:

Total Area (a) = 136

Total length (l) = 15 + x

Total width (w) = 6 + x

where x is the unknown length and width both in meters. Set up an equation for the total area now! We have:

A = (l)(w)

136 = (15 + x) (6 + x)

Solve by multiplying, setting the equation equal to zero, and solving for the roots. **DISCLAIMER: Dimensions in real life are not negative! Choose the correct root (positive). Make sure to plug x in for the total width.

Let me know if you have questions!