Answer:
The value of x is 3
Step-by-step explanation:
Let us study the face of the cuboind
∵ The cuboid has 6 rectangular faces
∵ Each opposite faces area equal in areas
∴ 2 faces of dimensions 10 cm and 2 cm
∴ 2 faces of dimensions 10 cm and x cm
∴ 2 faces of dimensions 2 cm and x cm
∵ The total surface area of the cuboid is the sum of the areas of the 6 faces
∵ The area of the rectangle = length × width
∴ The total surface area = 2(10 × 2) + 2(10 × x) + 2(2 × x)
∴ The total surface area = 2(20) + 2(10x) + 2(2x)
∴ The total surface area = 40 + 20x + 4x
→ Add the like terms 20x and 4x
∴ The total surface area = 40 + 24x
∵ The total surface area of this cuboid is 112 cm²
→ Equate the two sides of the total surface area
∴ 40 + 24x = 112
→ Subtract 40 from both sides
∵ 40 - 40 + 24x = 112 - 40
∴ 24x = 72
→ Divide both sides by 24
∴ x = 3
∴ The value of x is 3
