Question

the length of hypotenuse right of an isosceles right angled triangle is 12root2 cm, let us write by calculating what will be the area of the field.​

Answer 1

Answer:

Draw a right angled isosceles triangle with the equal sides labelled as a units long and the hypotenuse 16Rt2 units [where Rt represents the ‘root’ sign].

Using Pythagoras’ Theorem, (i.e., for a right angled triangle, the sum of the squares of the two shorter sides is equal to the hypotenuse squared) we can state that: a^2 + a^2 = (16Rt2)^2. We see that the left side of this equation simplifies to 2a^2 and the right hand side to 512.

So, 2a^2 = 512.

Now a deduction: The triangle is half the size of a square of side a units. This square’s area is a^2 square units. The triangle’s area is half this, i.e., (a^2)/2square units.

We see above that 2a^2 = 512, so halving both sides gives a^2 = 256, i.e., the square’s area is 256 square units.

As the triangle is half the size of the square, its area is half of 256 square units, i.e., 128 square units.

ANSWER: The area of the triangle is 128 square units

Step-by-step explanation: