# A Geometry problem involving triangles

by Soumya Das
(India)

ACEF and ACDB are rectangles. BDEF is a square and the length of each side is 1 unit. If BG has a length of a, then what will be the length of AB?

Solution

First, show that triangle ABG and triangle AFE are similar.

Angle A is the same for triangle ABG and triangle AFE

Similarly, angle F is the same for triangle ABG and triangle AFE

Since triangle ABG and triangle AFE have two angles that have the same measure, the last angle for these two triangles must be the same.

Therefore, triangle ABG and triangle AFE are similar.

Since triangle ABG and triangle AFE are similar, we can use proportion to find ? or the length of AB.

AB/a = (AB + 1)/1

AB × 1 = a × AB + a × 1

AB = a(AB) + a

AB - a(AB) = a

AB(1-a) = a

AB(1-a)/(1-a) = a/1-a

AB = a/1-a

## Recent Articles

1. ### How To Find The Factors Of 20: A Simple Way

Sep 17, 23 09:46 AM

There are many ways to find the factors of 20. A simple way is to...

2. ### The SAT Math Test: How To Be Prepared To Face It And Survive

Jun 09, 23 12:04 PM

The SAT Math section is known for being difficult. But it doesn’t have to be. Learn how to be prepared and complete the section with confidence here.