Question

In right angled triangle the hypotenuse is 10cm more than the shorter side.if third side is 6cm less than hypotenuse,find the sides of right angled triangle

Answer 1

Answer:

Step-by-step explanation:

Given In right angled triangle the hypotenuse is 10 cm more than the shorter side.if third side is 6 cm less than hypotenuse,find the sides of right angled triangle

Let the length of shorter side be x cm

Now length of hypotenuse is 10 cm more than x, so it will be x + 10 cm

Given length of third side is 6 cm less than hypotenuse , so it will be x + 10 - 6 = x + 4 cm

We know that Pythagoras theorem states that the square on the hypotenuse is equal to the sum of the squares on the other two sides.

So (x + 10)^2 = x^2 + (x + 14)^2

We get  x^2 - 12 x - 84 = 0

We know x = - b ± √b^2 - 4 ac / 2 a

        x = 12 ± √144 + 336 / 2

        x = 16.9 cm

So we get shorter side as 16 .9 cm

Now hypotenuse = x + 10 = 16.9 + 10 = 26.9 cm

and third side = x + 4 = 16.9 + 4 = 20.9 cm

So sides are 16.9 cm, 26.9 cm and 20.9 cm

Answer 2

Answer:

Shorter side = 16.955 cm

Third side = 20.955 cm

hypotenuse = 26.955 cm

Step-by-step explanation:

In right angled triangle the hypotenuse is 10cm more than the shorter side.if third side is 6cm less than hypotenuse,find the sides of right angled triangle

Let say shorter Side = x cm

Hypotenuse = x + 10 cm

Third Side = hypotenuse - 6 cm =  x + 10 - 6 = x + 4 cm

in right angle triangle applying Pythagoras theorem

hypotenuse² = Base² + height²

(x+10)² = x² + (x+4)²

=> x² + 100 + 20x = x² + x² + 16 + 8x

=> x² -12x - 84 = 0

=> x = (12 ± √(144 + 336)  )/2

=> x = (12 ± 21.91)/2

=> x = 16.955   as x can not be negative

Shorter side = 16.955 cm

Third side = 20.955 cm

hypotenuse = 26.955 cm