document.write( "Question 234520: What is the perimeter and area of a rectangle with a side of 7ft and a diagonal of 25ft? \n" ); document.write( "
Algebra.Com's Answer #172916 by nyc_function(2741)![]() ![]() You can put this solution on YOUR website! We are given one side and a diagonal.\r \n" ); document.write( "\n" ); document.write( "We can think of the side as one of the legs of a right triangle and the diagonal as the hypotenuse of the same right triangle.\r \n" ); document.write( "\n" ); document.write( "We need to find the other leg as step one.\r \n" ); document.write( "\n" ); document.write( "To do this, we use the Pythagoren Theorem from geometry.\r \n" ); document.write( "\n" ); document.write( "(leg)^2 + (leg)^2 = (hypotenuse)^2\r \n" ); document.write( "\n" ); document.write( "(leg)^2 + 7^2 = 25^2\r \n" ); document.write( "\n" ); document.write( "(leg)^2 + 49 = 625\r \n" ); document.write( "\n" ); document.write( "(leg)^2 = 625 - 49\r \n" ); document.write( "\n" ); document.write( "(leg)^2 = 576\r \n" ); document.write( "\n" ); document.write( "Take square root of both sides.\r \n" ); document.write( "\n" ); document.write( "leg = 24\r \n" ); document.write( "\n" ); document.write( "So, the other side of the rectangle is 24 feet.\r \n" ); document.write( "\n" ); document.write( "We now use two formulas:\r \n" ); document.write( "\n" ); document.write( "To find the area, use A = length times width.\r \n" ); document.write( "\n" ); document.write( "To find the perimeter use, P = 2(length) + 2(width).\r \n" ); document.write( "\n" ); document.write( "A = 7 times 24\r \n" ); document.write( "\n" ); document.write( "A = 168ft^2\r \n" ); document.write( "\n" ); document.write( "===================================================\r \n" ); document.write( "\n" ); document.write( "P = 2(24) + 2(7)\r \n" ); document.write( "\n" ); document.write( "P = 48 + 14\r \n" ); document.write( "\n" ); document.write( "P = 62 feet\r \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " |