Math Problem Statement

Seorang tukang kayu ingin membina satu struktur pergola. Berapakah panjang setiap struktur sokongan yang diperlukan oleh tukang kayu tersebut?

Solution

The question in the image asks to calculate the length of the "struktur sokongan" (support structure) required for the wooden pergola, based on the given dimensions.

From the diagram:

  • The pergola is 2.3 meters tall.
  • The horizontal distance between the points connecting the structure is 1 meter.
  • The vertical height between the top and the connection point for the support structure is 2 meters, meaning the support structure spans the difference of 0.3 meters in height (2.3 m - 2.0 m).

This forms a right-angled triangle, where:

  • The vertical side is 2.3m2.0m=0.3m2.3 \, m - 2.0 \, m = 0.3 \, m.
  • The horizontal side is 1m1 \, m.

Now, we can calculate the length of the support structure using the Pythagorean theorem:

L=(1m)2+(0.3m)2L = \sqrt{(1 \, m)^2 + (0.3 \, m)^2}

I'll calculate that now.The length of each support structure ("struktur sokongan") required for the pergola is approximately 1.04 meters.

Would you like more details or have any further questions?

Here are some related questions:

  1. How does the Pythagorean theorem apply to real-life structures?
  2. How can you calculate the height of a structure if given other dimensions?
  3. What are the common materials used in building pergolas?
  4. How does the angle between the support structure and the pergola affect stability?
  5. How do you estimate the total material required for constructing a pergola?

Tip: When building structures, ensure all dimensions are accurate to maintain safety and structural integrity.

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Math Problem Analysis

Mathematical Concepts

Geometry
Right Triangle
Pythagorean Theorem

Formulas

Pythagorean Theorem: a^2 + b^2 = c^2

Theorems

Pythagorean Theorem

Suitable Grade Level

Grades 7-9