top button
Flag Notify
    Connect to us
      Site Registration

Site Registration

If lengths of sides AB, BC and AC of a right angle triangle are in a GP, what is the ratio between AC and AB?

+1 vote
348 views

If lengths of sides AB, BC and AC of a right angle triangle are in a geometric progression, what is the ratio between AC and AB?

Right Angle Triangle

posted Feb 16, 2017 by anonymous

Share this puzzle
Facebook Share Button Twitter Share Button LinkedIn Share Button

1 Answer

+2 votes

Thanks for the query.

One way to proceed as below -

let the sides AB, BC & CA be a/r, a and a*r respectively where r is the c.r.
hence, ratio of CA and AB is (a*r) / (a/r) = r^2
Now,
As per Pythagoras' theorem

(a/r)^2 + a^2 = (a*r)^2
cancelling a^2 we get,
(1/r)^2 + 1 = r^2 or, r^4 - r^2 - 1 = 0
solving for r^2 we get,
r^2 = (1/2) +/ - sqrt (5) / 2
Ignoring the - sqrt (5) / 2
we get the ratio as (1/2) + sqrt(5)/2

answer Feb 17, 2017 by Indranil Datta



Similar Puzzles
0 votes

Triangle ABC has a right angle at B. Let Q be along BC and P be along AB such that AQ bisects angle A and CP bisects angle C. If AQ = 9 and CP = 8√2, what is the length of the hypotenuse AC?
enter image description here

+1 vote

In a Right angle triangle ABC

AB=3,AC=4 & BC=5

at BC,E is middle point and D is altitude AD

Find distance DE=?

it is not a difficult question everyone who know maths ...
Can YOU solve it easily ...... solve it in one line...........or in second..........?

0 votes

A triangle with sides AB = 3, BC = 4, and AC = 5 has an inscribed square PQRS with side QR along the side AC.
What is the area of the square?

enter image description here

0 votes

If in a right angle triangle the lengths of the two sides including the right angle are 27 and 120 units long, how many units is the third side?

...