Question

one side of a right angles triangle is thrice the other and the hypotenuse is 12cm .the area of the triangle.​

Answer 1

Step-by-step explanation:

the value of one side is 6 so the value of other side is 3x= 3 x 6 = 18

Answer 2

The Area Of the Triangle is 36cm²

GIVEN:

Length of hypotenuse = 12cm

Value of one side is 3 times the value of other side.

TO FIND

Area of the triangle.

SOLUTION:

We can easily solve the problem as under.

Let,

length of one side of the right angled triangle = a

length of another side will be, 3a

To find the length of triangle,

we will apply Pythagoras' theorem -

Sum of square of sides of right angled triangle is equal to the square of hypotenuse.

that is,

${a}^{2} + {b}^{2} = {h}^{2}$

Putting the values in the above equation. -

${a}^{2} + {3a}^{2} = 12^{2}$

we can also write it as,

$4 {a}^{2} = 144$

${a}^{2} = \frac{144}{4}$

${a}^{2} = 36$

a = 6

So, length of one side = 6

length of another side = 6× 3 = 18

Area of a right angled triangle = 1/2 × base × height

putting the values in above equation,

$area \: of \: triangle \: = \frac{1}{2} \times 6 \times 18$

= 36

Hence Area Of Triangle = 36cm²