SOLUTION: Using a 4:3 ratio, determine the side lengths of a TV whose diagonal length is 55 inches.

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Question 1150626: Using a 4:3 ratio, determine the side lengths of a TV whose diagonal length is 55 inches.
Found 2 solutions by josmiceli, ikleyn:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +x+ = the length
Let +y+ = the width
----------------------------
(1) +4%2F3+=+x%2Fy+
(2) +x%5E2+%2B+y%5E2+=+55%5E2+
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(1) +x+=+%28+4%2F3+%29%2Ay+
(2) +x%5E2+%2B+y%5E2+=+55%5E2+
(2) +%28+%284%2F3%29%2Ay+%29%5E2+%2B+y%5E2+=+3025+
(2) +%28+16%2F9+%29%2Ay%5E2+%2B+%289%2F9%29%2A+y%5E2+=+3025+
(2) +%28+25%2F9+%29%2Ay%5E2+=+3025+
(2) +y%5E2+=+%28+9%2F25+%29%2A3025+
(2) +y+=+%28+3%2F5%29%2A55+
(2) +y+=+33+
and
(1) +x+=+%28+4%2F3+%29%2Ay+
(1) +x+=+%28+4%2F3+%29%2A33+
(1) +x+=+44+
---------------------------
The sides are 33 in and 44 in
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check:
+44%5E2+%2B+33%5E2+=+55%5E2+
+1936+%2B+1089+=+3025+
+3025+=+3025+
OK

Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
Diagonal divide the rectangle in two triangles, each of which is (3-4-5) right angled triangle.


Therefore, the dimensions of each triangle are 3x, 4x and 5x inches, where x is their common measure, now unknown.


We will find x very easy by noticing that 5x = 55 inches;  hence  x = 11 inches.


Therefore, the dimensions of the TV are  3*11 = 33 inches and  4*11 = 44 inches.    ANSWER


Solved (mentally).