Answer:
Perimeter of the cross section = (10+4√5)inches = 18.9in
Area of the cross section= = 10√5 in²
Explanation:
Find attached the diagrams used in solving the question
Dimensions of granite = 4in by 2in
Length = 4in
Breadth = 2in
Height = 5in
When granite is cut lengthwise along it's diagonal, the cross section formed by the cut will be a rectangle.
Perimeter of the cross section = 2(height+breadth)
Breadth = diagonal of the cross section
The diagonal of a rectangle divides the rectangle into two right angled triangles.
We would apply Pythagoras theorem to find the length of the diagonal
Hypotenuse ² = opposite ²+adjacent ²
Hypotenuse = length of diagonal
Hypotenuse ² = 2² + 4²
Hypotenuse ² = 4+16 = 20
Hypotenuse = √20 = 2√5
Perimeter of the cross section = 2(height+breadth) =2(5+2√5)
Perimeter of the rectangle = 10+4√5 inches = 18.9in
Area of the cross section= diagonal × height
Area of the cross section= 2√5 × 5
Area of the cross section= = 10√5 in²