Hypotenuse of right triangle is 2m longer'n shortest side;other leg's 1m longer'n shortest. Whats hypot length

Question

The hypotenuse of a right triangle is 2 meters longer than its shortest side. The other side is 1 meter longer than the shortest side. How long is the hypotenuse?

Answer 1

5

x^2 + (x+1)^2 = (x+2)^2

Solve for x and get x = 3. hyp = 3 + 2 = 5

Answer 2

H - hypotenuse, L - longer side, S - shorter side H^2 = L^2 + S^2 (Pythagoras) Let x = S. H = 2x -1 L = x+1 Substituting into equation above gives: (2x - 1) ^ 2 = (x+1)^2 + x^2 4x^2 - 4x + 1 = x^2 + 2x + 1 + x^2 4x^2 - x^2 - x^2 - 4x -2 x + 1 - 1 = 0 2x^2 -6 x = 0 2x ( x - 3) = 0 x(x-3) = 0 x = 0 or x =3. x = 0 is not physically sensible in this context, so x=3 Check... S=3 => H=2*3 -1 = 5. S=3 => L = 3+1 = 4 Triangle has side lengths 5, 4, 3 - a well know right angled triangle!

Answer 3

let x = the shortest side
let x+1= the other side
let x+2 = hypotenuse

so the formula is a^2 + b^2 = c^2

(x)^2 + (x+1)^2 = (x+2)^2
x^2 + x^2 + 2x +1 = X^2 +4x +4
2X^2 + 2x +1=X^2 +4x +4
X^2 -2X - 3= 0
now factor it

(x+1)(x-3)=0

x= -1 or 3
cant have a negative distance so x=3 meters
now add the 2 and you get 5 meters

Answer 4

Length of hypotenuse = x

(x-2)^2 + (x-1)^2 = x^2 (Pythagoras Theorem)

x^2 - 4x + 4 + x^2 - 2x + 1 = x^2

x^2 - 6x + 5 = 0

(x-1)(x-5)=0

x=1, x=5

Disregard x=1 as this implies sides are -1, 0 and 1 (sides must have positive length)

hypotenuse = 5m
other sides = 3m, 4m

Answer 5

shortest side = x
hypotenuse = x+2
other leg = x+1

hypotenuse^2 = bas^2 + perpendicular^2
(x+2)^2 = (x+1)^2 = x^2
=> x^2 +4x + 4x = x^2 + 1 + 2x + x^2
=> x^2 - 2x -3 = 0
=> (x^2 -3x) + (x-3) = 0
=> (x-3)(x+1) = 0

therefore, x = 3 or -1
because x cannot be -ve, so x=3m

hyp = x+2
hypotenuse = 5m

Answer 6

Let shortest side be x m
Other side = x + 1 m
Hypotenuse = x + 2 m
(x + 2)² = x² + (x + 1)²
x² + 4x + 4 = x² + x² + 2x + 1
x² - 2x - 3 = 0(
x - 3).(x + 1) = 0
x = 3 , x= -1
Taking x = 3, sides are
3m , 4m and 5m
Hypotenuse = 5m

Answer 7

x^2=the shortest side
x+1=the other side
x+2=the hypotenuse

x^2+(x+1)^2=(x+2)^2
x^2+x^2+2x+1=x^2+4x+4
2x^2+2x+1=x^2+4x+4
x^2-2x-3=0
(x+1)(x-3)=0
x=3

3+2=5 m. for the hypotenuse.