SOLUTION: find the length and width with a ratio of 16:9 of a rectangle that has a 42 inch diagonal

Question 271201: find the length and width with a ratio of 16:9 of a rectangle that has a 42 inch diagonal
Found 2 solutions by checkley77, dabanfield:
Answer by checkley77(12844) (Show Source): You can put this solution on YOUR website!
16^2+9^2=c^2 solution of a similar triangle.
256+81=c^2
c^2=337
c=sqrt337
c=18.35756 diagonal length.
42/18.35756=2.288 ans. for the multiplier.
16*2.288=36.608 ans. for the longer side.
9*2.288=20.592 ans. for the shorter side.
Proof:
36.608^2+20.592^2=42^2
1340.1456+424.03=1,764
1,764~1,764
Answer by dabanfield(803) (Show Source): You can put this solution on YOUR website!
find the length and width with a ratio of 16:9 of a rectangle that has a 42 inch diagonal
Let W be the width and L the length of the rectangle. We know then that:
16/9 = L/W
L = (16/9)*W
Then using the Pythagorean Theorem we have:
L^2 + W^2 = 42^2 and
[(16/9)*W]^2 + W^2 = 42^2
Solve the above for W and then calculate L = (16/9)*W
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