Match Area

The Geometric Mean

The geometric mean of and creates a square with the same area as an rectangle.

Area: {{ s1.a * s1.b }}
,
=
Area: {{ s1.userX * s1.userX }}
{{ s1.userX }}
Drag to resize square Match!
Scale to overlap

Three Similar Triangles

The altitude splits the right triangle into two smaller triangles. They are all similar (same shape, different size). Scale the small ones to prove it!

Big Triangle Big Triangle
Drag to build

Equal Ratios

Because they are similar, their sides form equal ratios:
Short Leg / Long Leg = Short Leg / Long Leg

Cross-multiply to get:
Slide to solve

Find the Lengths

x={{ p.x }} y={{ p.y }} h={{ s4.h || '?' }} a={{ s4.a || '?' }} b={{ s4.b || '?' }} c = {{ p.c }}
{{ s4.h }}
{{ s4.a }}
{{ s4.b }}

Mastered!

You successfully used the geometric mean to solve right triangles.

Key Formulas

  • Altitude:
  • Leg a:
  • Leg b: