Question

Why h² = p² + b²
Spammers will be reported ⚠
​

Answer 1

Answer:

Here this formula is related to Pythagorus theorem which states that in a right angled triangle square of hypotenuse is equal to sum of the squares of other two sides. In H2 = P2 + B2 H is hypotenuse, P is perpendicular side, B is base .

Answer 2

Given: A ∆XYZ in which ∠XYZ = 90°.

To prove: XZ² = XY² +YZ²

Construction: Draw YO ⊥ XZ

Proof: In ∆XOY and ∆XYZ, we have,

∠X = ∠X | Common

∠XOY = ∠XYZ | each equal to 90°

Therefore, ∆XOY ~ ∆XYZ | by AA-similarity

⇒ $\frac{XO}{XY} = \frac{XY}{XZ}$

⇒ XO × XZ = XY² ----------------- (i)

‎

In ∆YOZ and ∆XYZ, we have,

∠Z = ∠Z | Common

∠YOZ = ∠XYZ | Each equal to 90°

Therefore, ∆YOZ ~ ∆XYZ | by AA-similarity

⇒ $\frac{OZ}{YX} = \frac{YX}{XZ}$

⇒ OZ × XZ = YZ² ----------------- (ii)

‎

From (i) and (ii) we get,

XO × XZ + OZ × XZ = (XY² + YZ²)

⇒ (XO + OZ) × XZ = (XY² + YZ²)

⇒ XZ × XZ = (XY² + YZ²)

⇒ XZ²= (XY² + YZ²)

‎

Hence proved