Math, asked by speedoaustralia, 1 year ago

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!!)

Answers

Answered by abhi569
0
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



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

speedoaustralia: Yep... sorta...
abhi569: (-:
speedoaustralia: sorry, but can you explain why we do "+ 2( 1 × q )" step?
abhi569: In formula, ( a + b )² = a² + b² + 2( a × b)
abhi569: Hence, ( q + 1 )² = q² + 1² + 2( q × 1 )
abhi569: Now?
speedoaustralia: ohh. because i thought that it was (q+1)^2 = q^2+1^2 only
speedoaustralia: yeah now that i've learnt the formula, it is making much for sense... thanks for all the help
abhi569: Welcome
abhi569: (-:
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