pythagorean theorem: L:w = 4:3, diagonal 75; find length

[ally]

Having trouble with this problem:

The length and width of a rectangle are in the ratio of 4:3. If the length of the diagonal is 75, what is the length?

I know a square plus b square equal 75 square (5625)
but where do I go from there?

 

[stapel]

Now use the ratio they gave you. If the two sides are "a" and "b", and if they are in the ratio of 4 to 3, then a/b = 4/3, so a = (4/3)b. Plug "b" and "(4/3)b" into the Pythagorean Theorem, and solve the resulting equation for the value of "b". Back-solve for the value of "a".

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

 

[ally]

Re: pythagorean theorem

ok so I have 4/3 b square plus b square = 5625
4/3 plus 3/3 b square??????=5625

 

[DrMike]

Re: pythagorean theorem

ok so I have 4/3 b square plus b square = 5625

Yep, as long as "4/3 b square" means "(4/3 b) squared".

4/3 plus 3/3 b square??????=5625

Nope. (4/3 b) squared will be (16/9) b[sup:3k02i9uo]2[/sup:3k02i9uo]. So you get (16/9 + 9/9)b[sup:3k02i9uo]2[/sup:3k02i9uo]=5625.

Do you know what to do next?

 

[ally]

Re: pythagorean theorem

225?????

 

[Denis]

Re: pythagorean theorem

Quit guessing :shock:

You have:
(16/9 + 9/9)b^2=5625.

What's 16/9 + 9/9? 25/9, right?
So:
b^2 = 5625 / (25/9)

If you can't finish that, you need help from your teacher.

 

[Mrspi]

Re: pythagorean theorem

Having trouble with this problem:

The length and width of a rectangle are in the ratio of 4:3. If the length of the diagonal is 75, what is the length?

I know a square plus b square equal 75 square (5625)
but where do I go from there?

Here's a slightly different approach.

Since the length and width are in the ratio of 4:3, you could
let 4x = length
and
let 3x = width

Now, the length and width are the two legs of a right triangle whose hypotenuse is 75.

leg[sup:uenso9jr]2[/sup:uenso9jr] + leg[sup:uenso9jr]2[/sup:uenso9jr] = hypotenuse[sup:uenso9jr]2[/sup:uenso9jr]

(4x)[sup:uenso9jr]2[/sup:uenso9jr] + (3x)[sup:uenso9jr]2[/sup:uenso9jr] = 75[sup:uenso9jr]2[/sup:uenso9jr]

Can you take it from here and find the value of x? Then, remember that the problem asks you for the length of the rectangle...that's 4x.