Math Problem Statement

The diagonal of this rectangle is 17 cm long and one leg is 8 cm long. How long is the other side?

Solution

We can use the Pythagorean theorem to solve this problem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the diagonal in this case) is equal to the sum of the squares of the lengths of the other two sides.

The formula is: a2+b2=c2a^2 + b^2 = c^2 where:

  • aa and bb are the lengths of the two legs (sides of the rectangle),
  • cc is the length of the hypotenuse (the diagonal).

Given:

  • The diagonal c=17c = 17 cm,
  • One leg a=8a = 8 cm,
  • The other leg bb is unknown.

Now, substituting the known values into the Pythagorean theorem:

82+b2=1728^2 + b^2 = 17^2 64+b2=28964 + b^2 = 289 b2=28964b^2 = 289 - 64 b2=225b^2 = 225 b=225=15b = \sqrt{225} = 15

So, the length of the other side is 1515 cm.

Let me know if you would like further details or clarification!


Here are 5 related questions to explore:

  1. What is the Pythagorean theorem, and how does it apply to triangles?
  2. Can the Pythagorean theorem be used for non-right-angled triangles?
  3. How do you calculate the diagonal of a rectangle if the two sides are known?
  4. What is the relationship between the sides of a 3-4-5 triangle?
  5. How do you determine the hypotenuse if the legs are known in a right triangle?

Tip: To remember the Pythagorean theorem, think of it as finding the "missing" side of a triangle when two sides are known. The equation always relates the squares of the sides.

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Math Problem Analysis

Mathematical Concepts

Geometry
Pythagorean Theorem
Right Triangles

Formulas

a^2 + b^2 = c^2

Theorems

Pythagorean Theorem

Suitable Grade Level

Grades 6-8