Answer: the sand in the new terrarium is 2 inches deep.
Step-by-step explanation:
Zach has a terrarium with the dimensions of 20 by 8 and the terrarium was filled with 3 inches of sand. It means that the volume of sand that this terrarium contains is
20 × 8 × 3 = 480 inches³
Zach gets a new terrarium that is larger with the dimensions of 10 by 24. If Zach moved the existing sand in the new terrarium and the height of the sand is represented by h, then the volume of sand into he new terrarium is
10 × 24 × h = 240h
Since the volume of sand in both terrariums is equal, then
240h = 480
h = 480/240
h = 2 inches
Answer:
The area of the rectangle = 50 cm^2.
Step-by-step explanation:
Let the shortest side of the rectangle be x cm.
Perimeter of the rectangle is:
2x + 2(x + 5).
Perimeter of the triangle = 3 * 2x.
As they have the same perimeter:
2x + 2(x + 5) = 3*2x
2x + 2x + 10 = 6x
6x - 2x - 2x = 10
2x = 10
x = 5 cm.
So the area of the rectangle = x(x + 5)
= 5 * 10
= 50 cm^2.
Option D:
The approximate area of the figure is 109.6 square feet.
Solution:
The figure is splitted into three shapes.
One is rectangle and the other two is semi-circles.
Diameter of the semi-circle = 5 feet
Radius of the semi-circle = 5 ÷ 2 = 2.5 feet
Area of the semi-circle = 

Area of the semi-circle = 9.8 square feet
Area of 2 semi-circles = 2 × 9.8
Area of 2 semi-circles = 19.6 square feet
Length of the rectangle = 18 feet
Width of the rectangle = 5 feet
Area of the rectangle = length × width
= 18 × 5
Area of the rectangle = 90 square feet
Area of the figure = Area of 2 semi-circles + Area of the rectangle
= 19.6 square feet + 90 square feet
= 109.6 square feet
The approximate area of the figure is 109.6 square feet.
Hence Option D is the correct answer.