Special Right Triangles Math Example 3

Follow the full solution, then compare it with the other examples linked below.

Example 3

easy
The diagonal of a square is 10 cm. Find the side length of the square.

Solution

  1. 1
    Step 1: The diagonal of a square divides it into two 45-45-90 triangles, where the diagonal is the hypotenuse.
  2. 2
    Step 2: Using the ratio 1:1:21:1:\sqrt{2}, if the hypotenuse is 10, then the side length =102=1022=52≈7.07= \frac{10}{\sqrt{2}} = \frac{10\sqrt{2}}{2} = 5\sqrt{2} \approx 7.07 cm.

Answer

Side length =52≈7.07= 5\sqrt{2} \approx 7.07 cm.
A square's diagonal creates two congruent 45-45-90 right triangles. The diagonal is the hypotenuse and equals s2s\sqrt{2}, where ss is the side length. Solving for ss gives s=diagonal2s = \frac{\text{diagonal}}{\sqrt{2}}.

About Special Right Triangles

Two families of right triangles whose side ratios can be determined exactly: the 30-60-90 triangle with sides in ratio 1:3:21 : \sqrt{3} : 2, and the 45-45-90 triangle with sides in ratio 1:1:21 : 1 : \sqrt{2}.

Learn more about Special Right Triangles →

More Special Right Triangles Examples

Example 1 easy

A 45-45-90 triangle has legs of length 7. Find the length of the hypotenuse.

Example 2 medium

In a 30-60-90 triangle, the hypotenuse is 16. Find the lengths of both legs.

Example 4 hard

An equilateral triangle has side length 12. Find its height and area using the 30-60-90 triangle rel

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