SOLUTION: The diagonal of a television set is 52 inches long. Its length is 28 inches more than its height. Find the dimensions of the television set.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: The diagonal of a television set is 52 inches long. Its length is 28 inches more than its height. Find the dimensions of the television set.      Log On


   

Question 249403: The diagonal of a television set is 52 inches long. Its length is 28 inches more than its height. Find the dimensions of the television set.
Found 3 solutions by user_dude2008, checkley77, oberobic:
Answer by user_dude2008(1862) About Me  (Show Source):
You can put this solution on YOUR website!
L^2+H^2=52^2

(H+28)^2+H^2=52^2

H^2+56H+784+H^2=2704

2H^2+56H-1920=0

2(H+48)(H-20)=0

Answers: H=20, L=48



Answer by checkley77(12844) About Me  (Show Source):
You can put this solution on YOUR website!
(28+x)^2+x^2=52^2
784+56x+x^2+x^2=2,704
2x^2+56x+784-2,704
2x^2+56x-1,920=0
2(x^2+28x-960)=0
2(x-20)(x+48)=0
x-20=0
x=20 inches for the height
20+28=48 inches for the length.
Proof:
48^2+20^2=52^2
2,304+400=2,704
2,704=2,704

Answer by oberobic(2304) About Me  (Show Source):
You can put this solution on YOUR website!
The diagonal of the TV can be considered the hypotenuse of a right triangle. It can be solved using the Pythagorean formula:
C%5E2+=+A%5E2+%2B+B%5E2
.
Assuming L is the width of the TV set, which the problem calls "length", and H is the height of the screen.
L+=+H+%2B+28
.
Returning to the Pythagorean formula...
D+=+diagonal+=+52
.
D%5E2+=+L%5E2+%2B+H%5E2
.
Substituting L = H+28
D%5E2+=+%28H%2B28%29%5E2+%2B+H%5E2
52%5E2+=+%28H%2B28%29%28H%2B28%29+%2B+H%5E2
52%5E2+=+H%5E2+%2B+28H+%2B+28H+%2B+784+%2B+H%5E2
52%5E2+=+2H%5E2+%2B+56H+%2B+784
.
Squaring 52
2704+=+2H%5E2+%2B+56H+%2B+784
.
Dividing both sides by 2
1352+=+H%5E2+%2B+28H+%2B+392
.
Subtracting 1352 from both sides
0+=+H%5E2+%2B+28H+%2B+392+-+1352
.
Simplifying
0+=+H%5E2+%2B+28H+-960
.
Can 960 be factored such that the two terms are 28 apart?
Yes. 48*20 = 960 and 48-20=28
.
%28H%2B48%29%28H-20%29+=+0
.
So we have two candidate solutions: H= -48 and H = 20. Since a negative height is nonsense, then our suggested answer is:
H+=+20
.
Looking back to our defined equations,
L+=+H+%2B+28+=+20+%2B+28+=+48
.
Checking by using the Pythagorean formula:
D+=+52
L%5E2+=+48%5E2+=+2304
H%5E2+=+20%5E2+=+400
L%5E2+%2B+H%5E2+=+2704
sqrt%282704%29+=+52
.
So that checks just fine.
.
But is it an analog TV or an HDTV?
.
Analog TV has a ratio of width to height of 4:3. The picture is 4 units wide by 3 units high.
HDTV has a ration of 16:9. The picture is 16 units wide by 9 units high.
.
Our proposed TV set has a picture that is 48 wide by 20 high. That is a ratio of 48:20, or 24:10, or 12:5. This does not correspond to any real TV set. So perhaps a negative height would work when solving an "imaginary" TV problem. Hmmm...