The length of 
is given by the relationship between the similar triangles
ΔABD and ΔBDC.
- = <u>80</u>
Reasons:
The given parameters are;
The altitude of triangle ΔABD = 
The hypotenuse of formed right triangle = 
The length of AD = 8
Length of BD = 24
Whereby ΔABD is a right triangle
We have;
ΔABD is similar to ΔBDC
Therefore, by similar triangle proportional sides relationship, we have;
Which gives;
= 
Therefore;
Which gives;
Learn more about similar triangles here:
brainly.com/question/4618367
Hi there!
For any 45 45 90 right triangle, the length of the hypotenuse is always the square root of 2 times one of the legs.
To get the lengths of the leg, let's divide the length of the hypotenuse by the square root of 2.
We get the following:
When simplifying fractions like this, we want to avoid having radicals on the bottom. In order to remove the radical from the denominator, let's multiply the numerator and the denominator by the square root of 2.
We get the following:
That's your answer.
Have an awesome day! :)
- collinjun0827, Junior Moderator
Firstly, let's factorise each equation individually - to do this, find 2 numbers that when summed add to the value of the second term, and when multiplied give the value of the third term.
7 and 12 give us 4 and 3 (4+3=7, 4*3=12) -- 8 and 15 give us 5 and 3 (5+3=8, 5*3=15)
Now we can rewrite these equations as (y+4)(y+3) and (y+5)(y+3) respectively.
Putting this in a fraction: (y+4)(y+3)/(y+5)(y+3) -- We can clearly see that there is a y+3 on both sides of the fraction, and given there are no terms outside of the brackets being multiplied, we can directly cancel.
This gives us our final answer:
(y+4)/(y+5)
Combine like terms
8u+3u= 11u
and
9v-5v= 4v
So the answer is 11u+4v
