Marianna's rectangular garden is 15 yards long and 10 yards wide. She wants to stretch a wire for hanging lights from one corner of the garden to the opposite. About how long should the wire be?
The nearest would be 18. Right?
Right.
Pythagorean Theorem:
Let c equal the hypotenuse.
a^2 + b^2 = c^2
15^2 + 10^2 = c^2
225 + 100 = c^2
325 = c^2
? = c
To find out how long the wire should be, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) equals the sum of the squares of the other two sides.
In this case, the rectangular garden forms a right-angled triangle with the wire being the hypotenuse. The two sides of the triangle are the length and width of the garden, which are 15 yards and 10 yards respectively.
So, we can find the length of the wire using the formula:
Hypotenuse^2 = Length^2 + Width^2
Substituting the values:
Hypotenuse^2 = 15^2 + 10^2
Hypotenuse^2 = 225 + 100
Hypotenuse^2 = 325
To find the approximate value of the length of the hypotenuse (wire), we can take the square root of both sides:
Hypotenuse ≈ √325
Hypotenuse ≈ 18.03 (rounded to two decimal places)
Therefore, the wire should be approximately 18.03 yards long.