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?
(I understand most of the steps, but get confused on some... please help!!)
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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
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
speedoaustralia:
Yep... sorta...
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sorry, but can you explain why we do "+ 2( 1 × q )" step?
In formula, ( a + b )² = a² + b² + 2( a × b)
Hence, ( q + 1 )² = q² + 1² + 2( q × 1 )
Now?
ohh. because i thought that it was (q+1)^2 = q^2+1^2 only
yeah now that i've learnt the formula, it is making much for sense... thanks for all the help
Welcome
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