Examkin

Question

Difficulty: EasyRight Triangles and the Pythagorean Theorem

A rectangular garden has a length of 1212 feet and a width of 55 feet. A gardener wants to place a straight wooden diagonal walk from one corner of the garden to the opposite corner. What is the length, in feet, of the diagonal walk?

  1. A
    1717
  2. B
    119\sqrt{119}
  3. 1313Answer
  4. D
    8.58.5

Answer

The length of the diagonal walk is 1313 feet.
The diagonal of the rectangular garden forms a right triangle with the garden's length and width acting as the legs. By applying the Pythagorean theorem, a2+b2=c2a^2 + b^2 = c^2, where a=5a = 5 and b=12b = 12, we get 52+122=25+144=1695^2 + 12^2 = 25 + 144 = 169. Taking the square root of 169169 gives 1313. Thus, the length of the diagonal walk is 1313 feet.

Step-by-Step Solution

1
Identify the right triangle formed by the length, width, and diagonal of the rectangle.
A right triangle is formed where the two legs are the length (1212 feet) and the width (55 feet), and the hypotenuse is the diagonal walk (dd).
The corners of a rectangle form 90∘90^\circ angles, making the diagonal the hypotenuse of a right triangle.
2
Apply the Pythagorean theorem, a2+b2=c2a^2 + b^2 = c^2, where a=5a = 5, b=12b = 12, and c=dc = d.
52+122=d25^2 + 12^2 = d^2
To relate the legs of a right triangle to its hypotenuse.
3
Simplify the equation to solve for dd.
25+144=d225 + 144 = d^2, which simplifies to 169=d2169 = d^2. Taking the square root of both sides gives d=13d = 13.
To find the numerical value of the hypotenuse.

Key Concept

Right Triangles and the Pythagorean Theorem
Estimated Time:45s
Rate this question

Topics

Right Triangles and the Pythagorean Theorem

More questions from this topic