Question

Find the length of the hypotenuse of a right triangle, the other two sides of which measure 9cm and 12cm.
plss full formula

Answer 1

Answer :

• The length of hypotenuse is 15cm

Given :

• The other two sides of which measures 9cm and 12cm

To find :

• length of the hypotenuse

Solution :

In a triangle,

• Let ∆ABC be right angled at B

then,

• AB = 12cm
• BC = 9cm
• AC = ? Hypothenuse

As we know that ,

By Pythagoras theorem,

• AC² = AB² + BC²

where , AB is 12 cm and BC is 9cm

Now we have to find the AC (hypotenuse)

⇢ AC² = (12)² + (9)²

⇢ AC² = 144 + 81

⇢ AC² = 225

⇢ AC = √225

⇢ AC = 15cm

Hence The length of hypotenuse is 15cm

Answer 2

$\dag\:\underline{\sf Assumption\::}$

$\sf\:Let\:∆ABC\:be\:right\:angled\:at\:B$

$\sf\:Let$

• $\sf\:AB=12\:cm$

• $\sf\:BC=9\:cm$

$\dag\:\underline{\sf To\:find\::}$

• $\sf\:Hypotenuse\:(AC) = ?$

$\dag\:\underline{\sf Solution \::}$

$\sf\:By\:Phythagoras\:Theorem$

$\large{\underline{\boxed{\mathrm\pink{Hypotenuse^{2}=Perpendicular^{2}+base^{2}}}}}$

$\sf↦\:AC^{2}=AB^{2}+BC^{2}$

$\sf↦\:AC^{2}=12^{2}+9^{2}$

$\sf↦\:AC^{2}=144+81$

$\sf↦\:AC^{2}=225$

Sending power 2 from LHS to RHS it becomes square root :

$\sf↦\:AC=\sqrt{225}$

$\sf↦\:AC=15\:cm$

The length of hypotenuse of a triangle is $\large{\underline{\boxed{\mathrm\pink{15\:cm}}}}$

• Thnku :)