Question

Area of a right triangle is 54 . If one of its legs is 12 cm long, its perimeter is:​

Answer 1

Answer:

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Step-by-step explanation:

Area of right triangle=1/2×b×h

= 54 =1/2×12×h

= h = 9 cm

we know that in a rt triangle

${h}^{2} = {side}^{2} + {side}^{2}$

=

${h}^{2} = {12cm}^{2} + {9cm}^{2}$

$= 144 {cm}^{2} + 81 {cm}^{2}$

$= 225 {cm}^{2}$

Therefore h =15cm

Now perimeter=15cm+9cm+12cm

= 36 cm

Answer 2

Answer:

Let two sides of the right angled triangle other than hypotenuse are 12 cm and y cm

Then

One will be height and other one will be base

Area of triangle = 54 cm^2

So, 1/2×12× (y) = 54

6y= 54

y = 54/6

y = 9

It means two sides of right angle triangle other than hypotenuse are 12 and 9

Perimeter of triangle = base +

height +

hypotenuse

According to Pythagoras theorem

(Hypo.)^2 = (base)^2 + (height)^2

(Hypotenuse)^2= (12)^2 + (9)^2

= 144 + 81

= 225

Hypotenuse = underoot 225

Hypotenuse = 15 cm

Perimeter of triangle = 15+12+9

=36 cm

Perimeter of triangle will be 36 cm.