SOLUTION: The diagonal of a rectangle has a length 50. If its legs are in the ratio 3:4 , what is its perimeter? Thank you!

Question 922349: The diagonal of a rectangle has a length 50. If its legs are in the ratio 3:4 , what is its perimeter? Thank you!
Found 2 solutions by MathLover1, MathTherapy:
Answer by MathLover1(20849) (Show Source): You can put this solution on YOUR website!

The diagonal of a rectangle has a length : then

If its legs and are in the ratio , then we have:
...solve for

what is its perimeter?
the diagonal of a rectangle along with the legs and forms a right angle triangle; so, usu Pythagorean theorem to find the length of the legs
....substitute and

...solve for

or
since we have a length, we don't need negative solution;
so,
now go back to , plug in and and calculate

now we know the length of the sides and we can calculate perimeter :

Answer by MathTherapy(10552) (Show Source): You can put this solution on YOUR website!

The diagonal of a rectangle has a length 50. If its legs are in the ratio 3:4 , what is its perimeter? Thank you!

Let the multiplicative factor be x
Then the shorter leg measures 3x, and the longer leg measures 4x
Using the pythagorean formula, we get:

x, or multiplicative factor = , or 10
Measure of shorter leg: 3(10), or 30 units
Measure of longer leg: 4(10), or 40 units
Perimeter of rectangle: 2(30 + 40), or 2(70), or units
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