Math Problem Statement

Find the other side of a rectangular field if one side measures 15 m and a diagonal as 17 m

Solution

To find the other side of the rectangular field, we can use the Pythagorean theorem, which states that in a right-angled triangle:

Diagonal2=Side 12+Side 22\text{Diagonal}^2 = \text{Side 1}^2 + \text{Side 2}^2

Given:

  • One side of the rectangle (Side 1) = 15 m
  • Diagonal = 17 m

Let the unknown side be xx (Side 2).

By the Pythagorean theorem:

172=152+x217^2 = 15^2 + x^2

289=225+x2289 = 225 + x^2

Now, solve for x2x^2:

x2=289225=64x^2 = 289 - 225 = 64

Take the square root of both sides:

x=64=8x = \sqrt{64} = 8

So, the other side of the rectangular field is 8 meters.

Would you like more details or have any questions?

Here are some related questions for further practice:

  1. What is the area of this rectangular field?
  2. What is the perimeter of the rectangular field?
  3. How would the result change if the diagonal was 20 m instead of 17 m?
  4. How can the Pythagorean theorem be applied to non-rectangular shapes?
  5. Can you derive the length of the diagonal if both sides of a rectangle are known?

Tip: Always check that the largest value in a right triangle is used for the diagonal when applying the Pythagorean theorem.

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Math Problem Analysis

Mathematical Concepts

Geometry
Right-Angle Triangle
Pythagorean Theorem

Formulas

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

Theorems

Pythagorean Theorem

Suitable Grade Level

Grades 6-8