Math, asked by datgurl1858, 9 months ago

The hypotenuse of a right triangle is 10cm long. If one leg is 2 units longer than the other leg, then how long is the longer leg?

Answers

Answered by EliteSoul
65

Given

Hypotenuse of right angled ∆ = 10 cm.

One leg of ∆ is 2 units longer than the other leg.

To find

Length of longer leg of

Solution

Let the length of shorter leg be y cm & length of longer leg be (y + 2) cm.

We know that in a right angled :

⇒ Hypotenuse² = Base² + Altitude²

Putting values :

⇒ (10)² = y² + (y + 2)²

⇒ 100 = y² + y² + 4y + 4

⇒ 2y² + 4y + 4 = 100

⇒ 2(y² + 2y + 2) = 100

⇒ y² + 2y + 2 = 100/2

⇒ y² + 2y + 2 - 50 = 0

⇒ y² + 2y - 48 = 0

⇒ y² + 8y - 6y - 48 = 0

⇒ y(y + 8) - 6(y + 8) = 0

⇒ (y + 8)(y - 6) = 0

⇒ y = -8 or, y = 6 [Ignoring negative one]

y = 6

Finding legs of :

⇾ Shorter leg = y = 6 cm.

⇾ Longer leg = (y + 2) = 6 + 2 = 8 cm.

Therefore,

Length of longer leg of triangle is 8 cm.

Answered by AdorableMe
121

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Given :-

◘ The hypotenuse of a right triangle is 10 cm long.

◘ One leg is 2 units longer than the other leg.

To find :-

The length of the longer leg.

Solution :-

\leadsto Let the length of the shorter leg be x units.

\leadsto Then the length of the longer leg becomes = 2 + x units.

\leadsto The length of the hypotenuse = 10 units.

As it is a right triangle, so we apply the Pythagoras Theorem* :

(H)² = (P)² + (B)²

⇒(10)² = (x)² + (x + 2)²

⇒100 = x² + x² + 4 + 4x

⇒100 = 2x² + 4x + 4

⇒x² + 2x + 2 = 50

⇒x² + 2x - 48 = 0

⇒x² + 8x - 6x - 48 = 0

⇒x(x + 8) - 6(x + 8) = 0

⇒(x + 8)(x - 6) = 0

⇒(x + 8) = 0 or (x - 6) = 0

⇒x = -8 units or x = 6 units

Length can never be negative.

So, the length of the shorter leg is x = 6 units.

Now, length of the longer leg = (x + 2) units = (6 + 2) units

\huge\boxed{= 8\ units}

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* Pythagoras Theorem : The square of the length of the hypotenuse of a right triangle equals the sum of the squares of the lengths of the other two sides.

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