Question

A pool measuring 10 meters by 26 meters is surrounded by a path of uniform width if the area of the pool and the path combined is 612 square meters what is the width of the path

Answer 1

Answer: the width of the path is 4 meters.

Step-by-step explanation:

Let x represent the width of the path.

A pool measuring 10 meters by 26 meters is surrounded by a path of uniform width. It means that the combined length of the pool and the path is (10 + 2x) meters.

Also, the combined width of the pool and the path is (26 + 2x) meters.

if the area of the pool and the path combined is 612 square meters, it means that

(10 + 2x)(26 + 2x) = 612

260 + 20x + 52x + 4x² = 612

4x² + 72x + 260 - 612 = 0

4x² + 72x - 352 = 0

Dividing through by 4, it becomes

x² + 18x - 88 = 0

x² + 22x - 4x - 88 = 0

x(x + 22) - 4(x + 22) = 0

x - 4 = 0 or x + 22 = 0

x = 4 or x = - 22

Since the width cannot be negative, then x = 4

Answer 2

Answer:

4 meters

Step-by-step explanation:

Given:

A pool measuring 10 meters by 26 meters.

The pool is surrounded by a path of uniform width.

Area of the pool and the path combined is 612 square meters.

Question asked:

What is the width of the path ?

Solution:

First of all we will calculate area of the rectangular pool:-

Given:

Length of pool = 26 meters.

Breadth of pool = 10 meters

Combined area of the pool and path is given = 612 square meter

Now, let width of path in meter = $x$

As given that  pool is surrounded by uniform width of path, so length and breadth will be increased by $x+x=2x$

Combined length = $26+2x$

Combined width = $10+2x$

$Combined\ area = Combined\ length\times Combined\ breadth$

$612=(26+2x)(10+2x)\\612=26(10+2x)+2x(10+2x)\\612=260+52x+20x+4x^{2} \\\\612=260+72x+4x^{2}$

Subtracting both sides by 260

$352=4x^{2} +72x$

Subtracting both sides by 352

$0=4x^{2} +72x-352\\or\ 4x^{2} +72x-352=0$

Taking 4 as common:

$x^{2} +18x-88=0$

$x^{2} +22x-4x-88=0$

Taking common term $x+22$

$x(x+22)-4(x+22)=0$

$(x+22)(x-4)=0\\x+22=0, x-4=0$

$x=-22,\ x=4$

As width of path can never be in negative,

Therefore, width of the path  is 4 meters