+0  
 
+1
293
1
avatar

Right triangle ABC has one leg of length 6 cm, one leg of length 8 cm, and a right angle at A. A square has one side on the hypotenuse of triangle ABC and a vertex on each of the two legs of triangle ABC. What is the length of one side of the square in cm? Express your answer as a common fraction. 

 

Guest Feb 13, 2018
 #1
avatar+89781 
+2

Here's my solution

 

AB  = 6, BC   = 10 and  AC  = 8

Call the point where the upper left vetex of the triangle meets the triangle  = D

Call the point where the upper right vertex of the triangle meets the triangle = F

Call the point where the bottom left vertex of the square meets the triangle = E

 

And we have three congruent triangles   ABC  ~ ADF  ~ EBD

 

Let  the side of the square  = x = DF    and let AD  = y

And we have that

DF / AD  = BC / AB

x / y   =   10/6     ⇒  y = (3/5)x

 

And 

BD / DE   = BC / AC

 

[ 6 - y ] / x  =  10 / 8        subbing for y, we have that

 

[6  -  (3/5)x ] / x  =  10 / 8  =  5/4

 

Cross-multiply

 

4 [ 6  - (3/5)x ]  = 5x

 

24  -  (12/5)x  =  5x

 

24  =  5x +  (12/5)x

 

24  =  [ 25  + 12]x / 5

 

120  = 37 x

 

x  ⇒  120 / 37    =   side of the square 

 

 

cool cool cool

CPhill  Feb 14, 2018
edited by CPhill  Feb 14, 2018
edited by CPhill  Feb 14, 2018

35 Online Users

avatar

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.