Final answer:
The maximum diagonal length of a TV that Jake can purchase for his cabinet is 73 inches.
Step-by-step explanation:
To find the maximum diagonal length of a TV that Jake can purchase for his cabinet, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b). In this case, the width of the cabinet (48 inches) is one side of the triangle and the height of the cabinet (55 inches) is the other side. Let's calculate the diagonal length using the Pythagorean theorem:
a^2 + b^2 = c^2
48^2 + 55^2 = c^2
2304 + 3025 = c^2
5329 = c^2
c = sqrt(5329)
c ≈ 73 inches
Therefore, the maximum diagonal length of a TV that Jake can purchase for his cabinet is 73 inches.