Question

The perimeter of a right angled triangle is 70 units and its hypotenuse is 29 units. find the length of other sides

Answer 1

let the length of one of the sides be x and the other be y
given, hypotenuse = 29 units and perimeter= 70 units
x+y+hypotenuse = 70
x+y+29 = 70
x+y= 41
y = 41-x
by using pythagoras theorem
(hypotenuse)² = x²+y²
29² = x² + (41-x)²
841 = x² + x² -82x+ 1681
2x² -82x + 840= 0
x²-41x+420=0
x²-21x-20x+420=0
x(x-21)-20(x-21)= 0
(x-20)(x-21)=0
x=20                or       x=21
y=21                or       x=20
∴ the sides are 20 units and 21 units

Answer 2

Hypotenuse, c = 29 units
The other sides be a & b
Therefore, a^2 + b^2 = c^2
=> (70-b-29)^2 + b^2 = 29^2
(since a+b+c =70 units)
=> 2b^2 - 82b + 840 = 0
=> b^2 - 41b + 420 = 0
=> b^2 - 20b - 21b + 420 = 0
=> (b - 20) (b - 21) = 0
So, b = 20, 21
& a = 70-20-29 = 21
Therefore, the other sides are 20 & 21 units.