document.write( "Question 266505: The perimeter of a rectangle is (A – 30) units and the diagonal is 13 units. The area of the rectangle is B square units. Find B \n" ); document.write( "

Algebra.Com's Answer #195811 by vksarvepalli(154) $\"\"$ $\"About$

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let the length of the rectangle be l units and breadth b units\r
\n" ); document.write( "\n" ); document.write( "given \r
\n" ); document.write( "\n" ); document.write( " perimeter 2(l+b) = A-30 units ------------------ 1\r
\n" ); document.write( "\n" ); document.write( "and diagonal sqrt(l^2+b^2) = 13 units ---------------- 2 \r
\n" ); document.write( "\n" ); document.write( " => l^2+b^2 = 169 \r
\n" ); document.write( "\n" ); document.write( "and we have area lb=B sq. units -------------------- 3\r
\n" ); document.write( "\n" ); document.write( "squaring eq.1 we get \r
\n" ); document.write( "\n" ); document.write( " 4[(l+b)^2] = (A-30)^2\r
\n" ); document.write( "\n" ); document.write( "=. 4[l^2+b^2+2lb] = (A-30)^2\r
\n" ); document.write( "\n" ); document.write( "but from eq.s 2 and 3\r
\n" ); document.write( "\n" ); document.write( "we get 4[169+2B] = (A-30)^2\r
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\n" ); document.write( "\n" ); document.write( "thus B = $\"%28%28%28A-30%29%5E2%2F4%29-169%29%2F2\"$ \n" ); document.write( "

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