Question

if two perpendicular sides of a right- angeled triangle are5cm and 12cm it's perimeter is how much

Answer 1

Step-by-step explanation:

Given :-

Two perpendicular sides of a right- angeled triangle are 5cm and 12cm.

To Find :-

Perimeter of the ∆

Solution :-

⋆ Let's say that, hypotenuse of the right angled ∆ is x cm.

$\pink{\bigstar \tt{ \: By \:using \: pythagoras \: theorem }}$

$\implies{ \tt{ {p}^{2} + {b}^{2} = {h}^{2} }}$

$\implies{ \tt{ {5}^{2} + {12}^{2} = {x}^{2} }}$

$\implies{ \tt{25 + 144 = {x}^{2} }}$

$\implies{ \tt{169 = {x}^{2} }}$

• Taking (square) ² to L. H. S.

$\implies{ \tt{ \sqrt{169} = x }}$

$\pink{\boxed{\implies{ \tt{13 = x}}}}$

Now,

We need to the perimeter of the ∆,

$\star{ \sf{ \: Perimeter \: of \: \triangle \: = \: Sum \: of \: all \: sides }}$

$\leadsto{ \sf{ \: Perimeter \: of \: \triangle \: = \: 5 + 12 + 13 }}$

$\leadsto{ \sf{ \: Perimeter \: of \: \triangle \: = 30 \: cm}}$

Henceforth,

$\underline{ \bf{ \star \:Perimeter \: of \: the \: right \: angled \: triangle \: is \: \pink{30 \: cm.}}}$