right triangle

Question

a toy manufacturer needs a toy in the shape of a right triangle with the longer leg 5cm more than the shorter leg and the hypotenuse 10cm more the the shorter leg. how long should the sides of the triangle be?

 

Answer 1

Short leg = x

Longer leg = x+5

hypotenuse = 10

 

By Pythagorean theorem

x² + (x+5)² = 10²

x² + x² + 10x + 25 = 100

2x² + 10x - 75 = 0

 

Use quadratic equation to solve for x

x = [-b±√(b²-4ac)]/2a , a=2, b=10, c = -75

 

x = [-10 ±√((10²-4(2)(-75))]/2(2)

 

  = [-10 ±√700]/4

  = (-10 ± 10√7)/4

 

Since the leg length will not be negative,

discard the negative...

 

x = (-10 + 10√7)/4 ≈ 4.1144 cm for shorter leg

 

x + 5 ≈ 9.1144 cm for longer leg

 

Check:  9.1144² + 4.1144² = 10²

            100.0006 = 100

 

As a rounding this is definitely close enough.

          

Answer 2

Shortest side =X

Longer side =X+5

Hypotenuse = X+10

For rt angle triangle

(X+10)² = X² + (x+5)² 

 

Gives X² -10X -75= 0

 

Solving this equation gives X = -5cm and  15cm

-5 can be ignored 

So shortest side = 15 cm

Hypotenuse = 25 cm and Third side = 20 cm