Math Problem Statement

Perbandingan panjang, lebar dan tinggi suatu balok adalah 5 : 3 : 2. Jika luas alas balok tersebut 135 cm², tentukan panjang, lebar dan tinggi balok tersebut!

Solution

The problem given is about a rectangular prism (box) with the ratio of its length, width, and height being 5:3:25:3:2. The area of the base (length ×\times width) of the box is given as 135 cm2135 \text{ cm}^2. We need to determine the dimensions of the box.

Let's denote the length, width, and height of the box as 5k5k, 3k3k, and 2k2k respectively, where kk is a scaling factor.

Given the area of the base: (5k)×(3k)=135 cm2(5k) \times (3k) = 135 \text{ cm}^2 15k2=13515k^2 = 135

We can solve for k2k^2 and subsequently for kk, then calculate the dimensions of the box: k2=13515k^2 = \frac{135}{15} k2=9k^2 = 9 k=9k = \sqrt{9} k=3k = 3

With k=3k = 3:

  • Length = 5k=155k = 15 cm
  • Width = 3k=93k = 9 cm
  • Height = 2k=62k = 6 cm

Thus, the dimensions of the box are:

  • Length: 15 cm
  • Width: 9 cm
  • Height: 6 cm

Would you like more details on this or have any other questions? Here are some related questions you might consider:

  1. How would you determine the volume of this box?
  2. What happens if the ratio of dimensions is changed?
  3. How would you solve this problem if only the volume and one dimension were given?
  4. Can you derive a general formula for the dimensions based on the area of the base and the ratio?
  5. What are the implications of using different units, such as meters instead of centimeters?

Tip: When given a problem involving ratios, it's often helpful to introduce a scaling factor, represented by kk, to easily manipulate and solve equations that involve proportions.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Ratios
Geometry
Algebra

Formulas

Length × Width = Area of the base
Scaling factor k: 5k, 3k, 2k for length, width, and height

Theorems

Area of a rectangle

Suitable Grade Level

Grades 7-9