Question

The smallest side of a right angle triangle is 4 less than his hypotenuse third side is two more than the smallest side .if the smallest side is x what is the other side write an equation find the length and breadth

Answer 1

Answer:

The dimensions of the triangle are 6cm, 8cm and 10cm.

Step-by-step explanation:

Let the length of the hypotenuse of the triangle be 'a'

and the length of the smallest side be 'x'

and the third side be 'c'

According to the conditions given in the question,

x = a - 4

c = x + 2  => x = c - 2

Equating both the equations, we get a - 4 = c - 2

=> a - c = -2 + 4 = 2

=> a = 2 + c

We know, by Pythagores Theorem,

Hypotenuse² = Base² + Perpendicular²

Substituting these values here, we get,

=> a² = x² + c²

=> (2 + c)² = (c - 2)² + c²

On opening the squares using the formula (a+b)² = a² + b² + 2ab

and (a-b)² = a² + b² - 2ab

=> 4 + c² + 4c = c² + 4 - 4c + c²

Cancelling the common terms, we get,

=>4c = - 4c + c²

=> 4c + 4c = c²

=> 8c = c²

=> c² -8c = 0

=> c(c - 8) = 0

Now either c=0 or c-8 =0

Now as length cannot be 0

Therefore, c-8 = 0

=> c = 8

As x = c - 2

=> x = 8 - 2 = 6

=> x =6

As a = 2 + c

=> a = 2 + 8

=> a = 10

Therefore, the dimensions of the triangle are 6cm, 8cm and 10cm.