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:

• 20 cm
• 48 cm
• 52 cm

GivEn :-

• A right angled triangle having perimeter 120 cm has perpendicular sides in the ratio 5:12.

To Find :-

• The sides

Step-by-step explanation:

The perpendicular sides are in ratio of 5 : 12

Let the common factor be x

Therefore, the perpendicular sides are 5x cm and 12x cm respectively.

According to the Pythagorus Theorem,

Hypotenuse² = Base² + Height²

➾ Hypotenuse² = (5x)² + (12x)²

➾ Hypotenuse² = 25x² + 144x²

➾ Hypotenuse² = 169x²

➾ Hypotenuse = 13x

➤ According to the question,

The perimeter of triangle is 120 cm

➾ 5x + 12x + 13x = 120

➾ 30x = 120

➾ x = 120 ÷ 30 = 4

Therefore, the sides are 20 cm, 48 cm and 52 cm.

Answer 2

$\huge {\underline {\underline \pink{ƛƝƧƜЄƦ}}}$

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.