Question 1132966
The perimeter of a right triangle with side lengths that are integers has the same area as a rectangle with dimensions 36 cm by 45 cm.
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Area = 36*45 = 1620
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Area of triangle = b*h/2 = 1620
b*h = 3240
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b^2 + h^2 = c^2, all integers
h = 3240/b
b^2 + (3240/b)^2 = c^2
b^4 + 10497600 = b^2c^2
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That's an ugly equation.
Try the commonly known right triangles with integers sides:
3-4-5
Area = 6
1620/6 = 270
3240/270 = 12  NG
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5-12-13
Area = 30
3240/30 = 108 NG
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8-15-17
Area = 60
3240/60 = 54 NG
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Find a right triangle with integer sides, and 3240/area is a perfect square.
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Here are some possibilities:
11:	60	:61	    
12:	35	:37
13:	84	:85
15:	112	:113
16:	63	:65
17:	144	:145
19:	180	:181
20:	21	:29
20:	99	:101
21:	220	:221
24:	143	:145	    
28:	45	:53
28:	195	:197
32:	255	:257
33:	56	:65
36:	77	:85
39:	80	:89
44:	117	:125
48:	55	:73
51:	140	:149
52:	165	:173	    
57:	176	:185
60:	91	:109
60:	221	:229
65:	72	:97
84:	187	:205
85:	132	:157
88:	105	:137
95:	168	:193
96:	247	:265
104:	153	:185
105:	208	:233
115:	252	:277
119:	120	:169
120:	209	:241
133:	156	:205
140:	171	:221
160:	231	:281
161:	240	:289
204:	253	:325
207:	224	:305
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It's possible that there is no solution, or that there's a mistake in the entry of the problem.