Question

A square garden has a diagonal of 34 ft. Colton wants to put a fence around the entire garden. The fencing is sold by the foot. What is the minimum amount of fencing he needs? 24 ft 25 ft 96 ft 97 ft.

Answer 1

A square can be identified(characterized) by its diagonal. The minimum amount of fencing needed by Colton for given context is: Option C: 96 ft

How to determine the minimum amount of fencing?

Since fencing is done all around the square garden, it must be at least of the length of the sum of all 4 sides of the garden. This quantity is actually called the perimeter of the square.

What is the perimeter and diagonal of a square?

Suppose that a square has side length 'a' units.

Then we get:

Diagonal of that square = $a\sqrt{2}$ units

Perimeter of that square = sum of all sides' lengths = a + a + a + a = 4a

For the given case, it is given that the square garden has got the length of its diagonal to be of 34 ft.  

Thus, if we suppose that the garden has its side length = 'a' feet, then

Diagonal is  $a\sqrt{2}$ feet

Thus,as both quantities of diagonals are same, thus,

$a\sqrt{2} = 34\\\\a = \dfrac{34}{\sqrt{2}} \approx 24.042 \: \rm feet$

Thus, the minimum amount of fencing for this garden = its perimeter = 4a

= 4 times 24.042  = 96.168 ≈ 96 feet

Thus, The minimum amount of fencing needed by Colton for given context is: Option C: 96 ft

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