Question

why h² = p² + b²
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Answer 1

Answer:

bcz of pythagoras theorem

Step-by-step explanation:

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

In a right angled triangle, the square of the hypotenuse is equal to the sum of the square of the remaining two sides that is base and perpendicular height.

Step-by-step explanation:

PYTHAGORAS THEOREM

GIVEN

∆ ABC

∠ ABC = 90°

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TO PROVE

AC² = AB² + BC²

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PROOF

In right angled triangle ABC, Seg BD ⊥ hypotenuse AC

∴ ∆ABC ~ ∆ADB ~ ∆BDC .....( By similarity of right angled triangle )

∆ABC ~ ∆ADB

$\frac{AB}{AD} = \frac{BC}{DB} = \frac{AC}{AB} - ( by \: corresponding \: sides )$

$\frac{AB}{AD} = \frac{AC}{AB}$

AB² = AC × AD .......... ( 1 )

Similarly, ∆ABC ~ ∆BDC

$\frac{AB}{BD} = \frac{BC}{DC} = \frac{AC}{BC} - ( by \: corresponding \: sides )$

$\frac{BC}{DC} = \frac{AC}{BC}$

BC² = DC × AC .......... ( 2 )

Adding ( 1 ) and ( 2 )

AB² + BC² = AD × AC + DC × AC

AB² + BC² = AC ( AD + DC )

AB² + BC² = AC × AC

∴ AB² + BC² = AC²

∴AC² = AB² + BC²

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LET'S SOLVE ONE EXAMPLE

Base = 3 cm

Perpendicular Height = 4 cm

Hypotenuse = ?

We know that,

Hypotenuse² = Base² + Height²

Hypotenuse² = ( 3 ) ² + ( 4 ) ²

Hypotenuse² = 25

Hypotenuse = √25

Hypotenuse = 5

Hypotenuse = 5 cm