Question

two perpendicular sides of a right angled triangle are in ratio 3:4 and its perimetre is 96 cm find the three sides

Answer 1

let one side be 3 and other side be 4 of a right angled triangle.
so,third angle = √(3²+4²)
= √(9+16) = √25
= 5
Now, let all sides be x ,
then ,perimeter = 3x + 4x+ 5x
= p = 12x
= 96 = 12 x
so,x = 8
hence ,All sides will be 24 ,32 and 40 .
hope it help....

Answer 2

$let \: the \: two \: perpendicular \: sides \: of \: a \: right \: angled \: triangle \: are \: in \: the \: ratio \: be \: x \\ \\ one \: side \: = 3x \\ two \: side \: = 4x \\ perimeter = 96cm \: \\ \\ 3 x \times 4x = 96 \\ 12x = 96 \\ x = \frac{96}{12} \\ x = 8cm \: \\ \\ one \: side = 3x = 3 \times 8 = 24cm \\ two \: side = 4x = 4 \times 8 = 32cm \:$