Question

A right-angled triangle has a hypotenuse of length p cm and one other side of length q cm. If p and q differ by 1, then the length of the remaining side, in centimetres, is

Answer 1

another side 1 cm will be the answer

Answer 2

Hypotenuse = p cm
Other side = q cm




Given, q + 1 = p

We know, hypotenuse² = height² + base²


=> ( p )² = ( q )² + ( base )²

=> ( q + 1 )² = q² + base²

=> q² + 1 + 2q = q² + base²

=> 1 + 2q = base²

=> 1 + q + q = base²

=> p + q = base² or remaining side²


=> √ ( p + q ) = remaining side


$=> \sqrt{p + q} \: \: cm = remaining \: side$







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