Question

A group of students in Math Class measured the area of their room, which is 24m⁴n⁴ - 42m³n³. Find the dimensions of the room.

A) Length: 2m²n², Width: 12m²n²
B) Length: 6m²n², Width: 4m³n³
C) Length: 6m²n², Width: 7m³n³
D) Length: 12m³n³, Width: 2m²n²

Answer 1

The dimensions of the room with an area of 24m⁴n⁴ - 42m³n³ are found by factoring out the common term, leading to dimensions of length 6m²n² and width 7m²n², corresponding to option C.

Step-by-step explanation:

The question asks to find the dimensions of a room given its area expressed in algebraic form as 24m⁴n⁴ - 42m³n³. To find the dimensions, we look for factors common to both terms of the expression. Both terms can be divided by 6m³n³, which gives:

24m⁴n⁴ / 6m³n³ = 4m
42m³n³ / 6m³n³ = 7n

Thus, the dimensions of the room could be 6m²n² for the length and 7m²n² for the width, which corresponds to option C.