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
Sep 17, 20 03:57 PM
Learn clearly the difference between discrete and continuous data with good examples.
Basic math formulas
Algebra word problems
New math lessons
Your email is safe with us. We will only use it to inform you about new math lessons.