Answer
4.) Option C is correct.
s = 15.5 cm
5.) Option C is correct.
r = 15.8 cm
Step-by-step explanation
We will use the concept of Pythagoras theorem to solve this.
The Pythagorean Theorem is used for right angled triangle, that is, triangles that have one of their angles equal to 90 degrees.
The side of the triangle that is directly opposite the right angle or 90 degrees is called the hypotenuse. It is normally the longest side of the right angle triangle.
The Pythagoras theorem thus states that the sum of the squares of each of the respective other sides of a right angled triangle is equal to the square of the hypotenuse. In mathematical terms, if the two other sides are a and b respectively,
a² + b² = (hyp)²
So, for the base of this box, we can see that s, w and l form a right angle triangle
a = w
b = l
hyp = s
a² + b² = (hyp)²
w² + l² = s²
w = 4 centimeters
l = 15 centimeters
w² + l² = s²
4² + 15² = s²
s² = 16 + 225 = 241
s² = 241
Take the square root of both sides
√s² = √241
s = 15.52 centimeters = 15.5 centimeters
The sides h, s and r form another right angle triangle
a = h
b = s
hyp = r
a² + b² = (hyp)²
h² + s² = r²
h = 3 centimeters
s = 15.52 centimeters = 15.5 centimeters
r = ?
3² + 15.52² = r²
9 + 241 = r²
r² = 250
Take the square root of both sides
√r² = √250
r = 15.81 centimeters = 15.8 centimeters
Hope this Helps!!!