Quadratic-fcns Qs: ratio of numbers is 1:3; triangle's sides

[jones19]

Hi, I actually heard about this site from a friend, I was doing a assignment and was stuck on two questions if someone could please assist me with this that would be great. The questions are :

1) Two positive integers are in the ratio 1:3. If their sum is added to their product the result is 224. Find the integers.

2) The difference between the length of the hypotenuse and the length of the next longest side of a right triangle is 2 cm. The difference between the lengths of the two perpendicular sides is 2cm. Find the three sides.

If someone could assist me that would be great. Thanks in advance.

PS. I am not sure if this is the right place to post this if a moderator decides to move plz inform me as well so I kno where my post is. Thanks

 

[Deleted member 4993]

Re: Two Quadratic fuctions question

Hi, I actually heard about this site from a friend, I was doing a assignment and was stuck on two questions if someone could please assist me with this that would be great. The questions are :

1) Two positive integers are in the ratio 1:3. If their sum is added to their product the result is 224. Find the integers.

2) The difference between the length of the hypotenuse and the length of the next longest side of a right triangle is 2 cm. The difference between the lengths of the two perpendicular sides is 2cm. Find the three sides.

If someone could assist me that would be great. Thanks in advance.

PS. I am not sure if this is the right place to post this if a moderator decides to move plz inform me as well so I kno where my post is. Thanks

You would have show your work and indicate exactly where you are stuck - so that we would know where to begin to help you.

 

[Loren]

Name things. In this case, you have two integers to name. Since they are in the ratio of 1 to 3, you could name one of them x and the other 3x. \(\displaystyle \frac{1x}{3x}=\frac{1}{3}\) so, we see they are in the ratio of 1 to 3. Now, build your equation and solve.

 

[stapel]

Note: In future, it will be helpful to show what you have tried, so the tutors can see where you're getting stuck. :wink:

1) Two positive integers are in the ratio 1:3. If their sum is added to their product the result is 224. Find the integers.

i) Pick variables for the two numbers.

ii) Using the variables in (i), form an equation reflecting the given ratio.

iii) Solve the proportion in (ii) for one of the variables in terms of the other.

iv) Write an expression for the sum, using the relationship found in (iii).

v) Write an expression for the product, using the relationship found in (iii).

vi) Add (iv) and (v), simplify, and set equal to the given result.

vii) Solve the equation in (vi). Test the solution(s) in the original exercise.

2) The difference between the length of the hypotenuse and the length of the next longest side of a right triangle is 2 cm. The difference between the lengths of the two perpendicular sides is 2cm. Find the three sides.

You know that the hypotenuse is the longest side. The "next longest side" is smaller, but larger than the third side.

i) Pick a variable for the length of the hypotenuse.

ii) Write an expression, in terms of (i), for the length of the "next longest side".

iii) Write an expression, in terms of (ii), for the length of the shortest side. Simplify.

iv) Plug the lengths of the sides into the Pythagorean Theorem.

v) Solve the equation in (iv) for the value of the variable in (i).

vi) Back-solve for the other side lengths.

If you get stuck, please reply showing how far you have gotten. Thank you!

Eliz.

 

[jones19]

thanks for all your help guys
special thanks to soroban he helpd me out via pm and it really helped thanks a lot.. i actually have one more question posted on viewtopic.php?t=26228
i have shown how far I have gotten if someone could assist me with that that would be great!
PS. my assignment is due tomorrow so help asap would be helpful. Thanks in advance

 

[stapel]

i actually have one more question posted on another thread ...if someone could assist me with that that would be great!

You've gotten lots of help in that thread. Please reply there,. showing what you have done.

Eliz.