Question

a right angle triangle is having perimeter 120 CM has its two perpendicular sides in the ratio 5 is to 12. find the length of its sides​

Answer 1

Answer:

AB=20

BC=48

AC=52

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welcome

Answer 2

Answer:

The lengths of its sides are 20 cm, 48 cm and 52 cm.

★ GivEn :-

• The perimeter of the right angle triangle is 120 cm.
• The triangle has its two perpendicular sides in the ratio 5 : 12.

★ To Find :-

• The lengths of its sides.

★ Solution :-

The triangle has its two perpendicular sides in the ratio 5 : 12.

Let the perpendicular sides be 5x cm and 12x cm. ( x is common factor where x > 0 )

We know that,

$\boxed { \red{ \sf \: Hypotenuse^{2} = side^{2} + side^{2} }}$

$:\implies \boxed { \sf \: Hypotenuse^{2} = (5x)^{2} + (12x)^{2} }$

$:\implies \boxed { \sf \: Hypotenuse^{2} = 25x^{2} + 144x^{2} }$

$:\implies \boxed { \sf \: Hypotenuse^{2} = 169x^{2} }$

$:\implies \boxed { \sf \: Hypotenuse = 13x}$

According to the question,

$\sf \: 5x + 12x + 13x = 120$

$\implies \: \sf \: 30x = 120$

$\implies \: \sf \: x = \cancel\dfrac {120}{30}$

$\implies \boxed{ \red{ \sf \: x = 4}}$

$\sf \: The \: length \: of \: the \: sides \: are,$

$\sf \: 5 \times 4 = 20 \: cm$

$\sf \: 12 \times 4 = 48 \: cm$

$\sf \: 13 \times 4 = 52 \: cm$