Question

El área de la superficie total de una caja de cartón es de 380cm^2, mide 4cm más de largo que de ancho y su altura es de 5cm. ¿Cuánto mide de largo y de ancho?

Answer 1

The dimensions are:

Length = 11.8 cm

Width = 7.8 cm

Height = 5cm

How to find the dimensions?

The surface area of a box of length L, width W, and height H is:

area = 2*(L*H + W*L + W*H)

Here we know that:

area = 380cm²

L = W + 4

H = 5cm

Then we can write the equation:

380cm² = 2*(L*5 + W*L + W*5)

380/2 = W*L + 5(L + W)

Now replace L by W + 4 in the equation, then we get:

190 = W*(W + 4) + 5*(W + 4 + W)

190 = W² + 4W + 10W + 20

0 = W² + 14W + 20 - 190

0 = W² + 14W - 170

The solutions are given by:

`W = (-14 \pm √(14^2 - 4*1*-170) )/(2*1) \\\\W = (-14 \pm 29.6 )/(2)`

We only can have a positive width, so:

W = (-14 + 29.6)/2 = 7.8

And thus:

L = 7.8 + 4 = 11.8