   Chapter 9.1, Problem 24E ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698

#### Solutions

Chapter
Section ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
1 views

# For a given box, the height measures 4 m. If the length of the rectangular base is 2 m greater than the width of the base and the lateral area L is 96 m2, find the dimensions of the box.

To determine

To find:

The dimensions of the box.

Explanation

The lateral area of any solid is the area of all the number of lateral sides that it have, excluding the area of the top and the bottom of the solid.

The lateral area (L) of any solid prison with the perimeter of the base of the prism as (P) and altitude ‘h’ is given by the formula,

L=Ph.

Here, P is the perimeter of any one of the base of the prism and which is given by the sum of all the sides of the base.

Calculation:

Given,

The height of the box =4 m.

The length is 2 m greater than the width and lateral surface area is 96 m2

Let ‘x’ be the width of the box.

Thus, we have the dimensions of the box as

l=x+2

w=x, and

h=4 m.

The lateral surface area of a prism with rectangular base (cuboid) is given by the formula

L=Ph

Here, ‘P’ is the perimeter of the base of the cuboid and ‘h’ is the altitude of the cuboid.

First let us find the perimeter of the base (Rectangular) of the cuboid box.

P=l+w+l+w

=2l+2w

P=2l+w

Now, substitute l=x+2 and w=x

P=2x+2+x

P=22x+2

P=2·2

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