Math Problem Statement

What is the length of leg s of the triangle below?

Solution

The triangle in the image is a 45°-45°-90° triangle, which is a special right triangle. In this type of triangle, the two legs are equal in length, and the relationship between the legs and the hypotenuse follows the ratio 1:1:21:1:\sqrt{2}.

From the image:

  • The hypotenuse is given as 18\sqrt{18}.

To find the length of the leg ss, we can use the following formula for 45°-45°-90° triangles:

Hypotenuse=s×2\text{Hypotenuse} = s \times \sqrt{2}

Given that the hypotenuse is 18\sqrt{18}, we substitute this into the formula:

18=s×2\sqrt{18} = s \times \sqrt{2}

Now, solve for ss:

s=182=182=182=9=3s = \frac{\sqrt{18}}{\sqrt{2}} = \frac{\sqrt{18}}{\sqrt{2}} = \sqrt{\frac{18}{2}} = \sqrt{9} = 3

So, the length of leg ss is 33.

The correct answer is D. 3.

Would you like more details or have any further questions?

Here are 5 related questions you might find interesting:

  1. How is the ratio 1:1:21:1:\sqrt{2} derived for a 45°-45°-90° triangle?
  2. Can the Pythagorean theorem be used to verify the result for a 45°-45°-90° triangle?
  3. How do special right triangles differ from general right triangles?
  4. What are the properties of other special triangles, such as 30°-60°-90° triangles?
  5. How can you generalize the formula for finding the legs of a right triangle given different angles?

Tip: In 45°-45°-90° triangles, knowing one leg allows you to find both the other leg and the hypotenuse easily using simple ratios!

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Geometry
Special Right Triangles

Formulas

Hypotenuse = s * sqrt(2)

Theorems

45°-45°-90° triangle theorem

Suitable Grade Level

Grades 8-10