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ICSE Class 9 Answered

1)The length of two sides of a right angled triangle containing the right angle differ by 6cm.If the area is 36cm2 find the perimeter

2)

Solve simultaneously

3/x+4y=7

5/x+6y=13

 

Asked by Sunita | 09 Mar, 2018, 02:40: PM
Expert Answer
begin mathsize 16px style Let space the space length space of space base equals straight x space cm
Then comma space height equals left parenthesis straight x minus 6 right parenthesis space cm
Now comma space area equals 36 space cm squared
rightwards double arrow 1 half cross times straight x cross times left parenthesis straight x minus 6 right parenthesis equals 36
rightwards double arrow straight x squared minus 6 straight x equals 72
rightwards double arrow straight x squared minus 6 straight x minus 72 equals 0
rightwards double arrow straight x squared minus 12 straight x plus 6 straight x minus 72 equals 0
rightwards double arrow straight x left parenthesis straight x minus 12 right parenthesis plus 6 left parenthesis straight x minus 12 right parenthesis equals 0
rightwards double arrow left parenthesis straight x minus 12 right parenthesis left parenthesis straight x plus 6 right parenthesis equals 0
rightwards double arrow straight x equals 12 space or space straight x equals negative 6
Rejecting space straight x equals negative 6 comma space since space length space of space straight a space side space cannot space be space negative.
straight x equals 12 space cm equals base
rightwards double arrow straight x minus 6 equals 12 minus 6 equals 6 space cm equals height
Thus comma space hypotenuse equals square root of 12 squared plus 6 squared end root equals square root of 144 plus 36 end root equals square root of 180 equals 6 square root of 5 space cm
Hence comma space perimeter equals 12 plus 6 plus 6 square root of 5 equals 18 plus 6 square root of 5 space space cm end style
 
Note: Please post one query at a time.
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