Question

An edge model of a cuboid is made from a 2.40 m long metal wire. Height and width are the same; the length is 6 cm greater than the width. The metal wire is completely used up. Find the width (x) of the cuboid.

Answer 1

The width of the cuboid is found to be 18 cm, after solving the equation derived from the dimensions provided and the total length of the wire.

Step-by-step explanation:

To find the width (x) of the cuboid when a 2.40 m long metal wire is used to create an edge model, we start by translating the problem into a mathematical equation. The perimeter (P) of a cuboid is given by P = 4(l + w + h) where l is the length, w is the width, and h is the height. According to the problem, the height and the width of the cuboid are the same (h = w), and the length is 6 cm greater than the width (l = w + 6 cm). Since we need to account for the entire wire, we will convert the wire's length from meters to centimeters: 2.40 m = 240 cm. The equation then becomes:

P = 4(w + w + (w + 6 cm))

P = 4(3w + 6 cm)

240 cm = 4(3w + 6 cm)

Now, we solve for w:

240 cm = 12w + 24 cm

216 cm = 12w

w = 18 cm

Therefore, the width of the cuboid is 18 cm.