Question

the altitude of a right angled traingle is 7 cm less than its base. if the hypotenuse is 13 cm long, then find two other sides

Answer 1

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Answer 2

Let its altitude be x cm
then base = x+7 cm
hypotenus=13 cm
by pythagoras theorem
${h}^{2} = {b}^{2} + {p}^{2}$
$169 = {(x + 7)}^{2} + {x}^{2} \\ 169 = {x}^{2} + 49 + 14x + {x}^{2} \\ 169 = 2 {x}^{2} + 49 + 14x \\ 2 {x}^{2} + 14x - 120 = 0$
solving the equation we can get
x=-12 and +5
so length cannot be negative hence altitude =5 and base =5+7=12