Question

$\bf \huge {\underline {\underline \red{QuEsTiOn}}}$

A right angled triangle having perimeter 120 cm has perpendicular sides in the ratio 5:12. Find the lengths of its sides​.​

Answer 1

Answer:

120÷3 40 if sides are equal this is the answer

but according to the question

consider the number of 5x and 12 x

so

5x + 12x is equals to 120

Answer 2

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Given

Perimeter of △= 120cm

Ratio of sides = 5 : 12

To Calculate

Length of all sides of △

Solution

Let the two sides be 5x and 12x

Now we will calculate third side using Pythagorous Theorem

$\bf\purple{ By\: Pythagorous\: Theorem }$

Let third side be y

$\bf Hypotenuse {}^{2} = Base{}^{2} + Perpendicular {}^{2}$

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

$\bf \implies {y}^{2} = {25x}^{2} + {144cm}^{2}$

$\bf \implies{y}^{2} = 169 {x}^{2}$

$\bf \implies y = \sqrt{169 {x}^{2} }$

$\bf \implies y = 13x$

$\bf \purple{\: Perimeter \: of \: triangle = 120cm}$

$\bf \implies 5x + 12x + y = 120$

$\bf \implies 5x + 12x + 13x = 120$

$\bf \implies 30x = 120$

$\bf \implies x = 120 \div 30$

$\bf \implies x = 4cm$

$\bf \blue{Therefore \: Sides \: are :-}$

5x = 5 × 4 = 20cm

12x = 12 × 4 = 48cm

13x = 13 × 4 = 52cm

Hence, sides of triangle are 20cm, 48cm and 52cm.