September 18th, 2015, 08:35 AM  #1 
Newbie Joined: Sep 2015 From: Dorset Posts: 4 Thanks: 0  Mum Needing Help  Find the length of the perpendicular height
Good evening all My daughter is only 11 and wants my help with homework but I am afraid I'm struggling. I have tried to google but I still do not understand. Rather than getting her to speak to her teacher I want to try and learn myself so I can help her. This is an example of what she needs to find out. I am not using the figures in her homework so she can work it out herself. Untitled.jpg So we have one big triangle with a triangle inside the triangle like in this picture. The left side of the large triange is 15cm The base is 8 cm The right side of the triangle is 17cm The black line inside the triangle is y (isn't very clear but it goes from the bottom right side of big triangle and across to the other side The question is find the length of the perpendicular height U in this triangle, write your answer to one decimal place I don't know if it matters but the top of the mini triangle is a right angle I hope you don't mind me posting to this forum. I use Mr Excel forum all the time so I am hoping this is the same type of thing Thank you From struggling mother! Last edited by alethea2000; September 18th, 2015 at 08:45 AM. Reason: to make it clearer 
September 18th, 2015, 08:38 AM  #2 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,958 Thanks: 1146 Math Focus: Elementary mathematics and beyond 
I'm not sure what you mean by "perpendicular height U". The diagram is not labelled.

September 18th, 2015, 08:39 AM  #3 
Newbie Joined: Sep 2015 From: Dorset Posts: 4 Thanks: 0 
let me see if I can get a clearer picture, sorry

September 18th, 2015, 08:47 AM  #4 
Newbie Joined: Sep 2015 From: Dorset Posts: 4 Thanks: 0 
is the picture above in the post any better? that is the question, find the length of the perpendicular height y in this triangle. I don't know if it means find the length of y or find out how tall the smaller triangle is 
September 18th, 2015, 08:58 AM  #5 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,958 Thanks: 1146 Math Focus: Elementary mathematics and beyond 
You may set up two equations: $\displaystyle a+b=17$ and $\displaystyle 225a^2=64b^2$, where $\displaystyle a$ and $\displaystyle b$ are the segments of the hypotenuse of the large triangle, as divided by y. 
September 18th, 2015, 09:01 AM  #6 
Newbie Joined: Sep 2015 From: Dorset Posts: 4 Thanks: 0 
I need to find a forum where I can understand the answers 
September 18th, 2015, 09:11 AM  #7 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,958 Thanks: 1146 Math Focus: Elementary mathematics and beyond 
Do you know the Pythagorean theorem?

September 18th, 2015, 11:00 AM  #8 
Senior Member Joined: Apr 2014 From: Europa Posts: 584 Thanks: 177  So we have one triangle ABC, $\displaystyle m(\hat{A})=90^0, AB=8cm, AC=15cm, BC=17cm \\\;\\ If \ AD\perp BC,\ D\in BC\ and\ AD=y,$ we must find y. We use formula: $\displaystyle AD=\dfrac{AB\cdot AC}{BC}=\dfrac{8\cdot15}{17}=\dfrac{120}{17} \approx 7.058 \approx 7.1cm \\\;\\ So,\ \ y \approx 7.1 cm$ 
September 18th, 2015, 01:42 PM  #9 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,958 Thanks: 1146 Math Focus: Elementary mathematics and beyond 
The formula aurel5 gave may be derived using the formula for the area of a triangle: the area of a triangle is one half of the base times the height  for the given triangle, the formula for area may be written in two ways. Setting them equal gives $\displaystyle \dfrac{17}{2}y=\dfrac{15\cdot8}{2}$ Solving for $\displaystyle y$: $\displaystyle y=\dfrac{120}{17}\approx7.1$ My apologies for making this problem more complicated that it needed to be. Last edited by greg1313; September 18th, 2015 at 01:45 PM. 
September 19th, 2015, 08:40 AM  #10 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 
The crucial point is that, since the nonright angles in a right triangle are complementary, the "large" triangle and two interior triangles are similar triangles they have the same angles and the various sides are in the same proportion. In particular, the ratio of shorter leg to longer is 8/15. The hypotenuse is divided by that perpendicular into two parts call the longer "y" so the shorter is 17 y. Equating the ratios of the smaller leg to longer in all three triangles, (17 y)x= x/y= 8/15. From x/y= 8/15, 15x= 8y. From (17 y)/x= 8/15, 15(17 y)= 8x. From 15x= 8y, y= (15/8 )x. Putting that into the second equation 15(17 (5/8 )x)= 255 (75/8 )x= 8x. Solve that equation for x. 

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