Question

the lengths of the sides of a triangle are 7cm 13cm and 12cm. find the length of a perpendicular from the opposite vertex to the side whose length is 12cm.

Answer 1

Answer:

Harmeet singh

Step-by-step explanation:

Answer 2

Answer:

$\red { Length \: of \:the \: altitude } \green {= 4\sqrt{3}\:cm }$

Step-by-step explanation:

In ∆ABC , AB = 7 cm, AC = 13 cm, BC = 12 cm .

AD is a perpendicular to BC.

Let BD = x cm, DC = (12-x) cm , AD = h cm .

i) In ∆ADB , <D = 90° .

AB² = BD² + AD² [ By

Pythagoras Theorem

=> 49 = x² + h²

=> h² = 49 - x² ---(1)

ii) In ∆ADC , <D = 90°,

AC² = AD² + DC²

=> 13² = h² + (12-x)²

=> 169 = 49 - x² + 12² - 2×12×x + x²

=> 169 = 49 + 144 - 24x

=> 24x = 193 - 169

=> 24x = 24

=> x = 1 ---(2)

Put x = 1 in eqution (1) , we get

=> h² = 49 - 1

=> h² = 48

$\implies h = \sqrt{48}\\= 4\sqrt{3}\:cm$

Therefore.,

$\red { Length \: of \:the \: altitude } \green {= 4\sqrt{3}\:cm }$

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