Question

Q19 The square of hypotenuse of right angled triangle is 50cm. If the two legs of right angled triangle is equal ,then the length of each leg is​

Answer 1

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Given:

• ∠ABC = 90°

• AC² = 50 cm

• AB = BC

To Find:

1. AB = ?
2. BC = ?

Method:

Since AB = BC and ∠ABC = 90°

Applying Pythagoras Theorem;

AC² = AB² + BC²

⇒ AC² = AB² + AB²

⇒ AC² = 2 AB²

⇒ 50 = 2 AB²

⇒ AB² = $\dfrac{50}{2}$ = 25

⇒ AB = $\sqrt{25} = 5 cm$

AB = BC = 5 cm

Additional Information:

Pythagoras Theorem states that:

In a Right Angled Triangle;

(Hypotenuse)² = (Base)² + (Perpendicular)²