Question

...answer it..........​

Answer 1

Answer is (iii)

By using pythagorous theorem,

(Hypotenuse)^2 = sum of squares of other two sides.

(2.5)^2 = (2)^2 + (1.5)^2

6.25 = 4 + 2.25

6.25 = 6.25 ——> Answer

Answer 2

$\mathcal{\green{\underline{\blue{GIVEN:}}}}$

The three sides are given.

$\mathcal{\green{\underline{\blue{TO \:\: FIND:}}}}$

Which of the following can be the sides of a right triangle.

$\mathcal{\green{\underline{\blue{SOLUTION:}}}}$

We can use Pythagoras theorem. If the numbers satisfy the theorem, they are right triangles. In other words, we are using the converse of Pythagoras theorem.

BASE²+HEIGHT²=HYPOTENUSE²

Now, how do we find out the hypotenuse? The longest side of all of them is the hypotenuse.

Let's apply Pythagoras theorem for (i):

$\to \sf 2.5^2+6^2=6.5^2$

$\to 6.25+36 = 42.25$

$\sf \to 42.25 \: units =42.25 \: units$

It is satisfying both sides of the equation. RHS=LHS. Thus, option 1 is correct, and we got our answer that 2.5, 6.5 and 6 can be the sides of a right triangle.

Never the less, I am solving the other two equations too!

Let's apply Pythagoras theorem for (ii):

$\sf \to 2^2+2^2=5^2$

$\sf \to 4+4=25$

$\sf \to 8 \: units \neq 25 \: units$

It is not satisfying both sides of the equation. RHS≠LHS. Thus, option (ii) is not correct, 2, 2 and 5 cannot be the sides of a right triangle.

Let's apply Pythagoras theorem for (iii):

$\sf \to 1.5^2+2^2=2.5^2$

$\sf \to 2.25+4=6.25$

$\to \sf 6.25 \: units = 6.25 \: units$

It is satisfying both sides of the equation. RHS=LHS. Thus, option (ii) is correct, 1.5, 2 and 2.5 can be the sides of a right triangle.

$\huge\underline\mathfrak\purple{Option \:\: (i) \:\: and \:\: (iii) \:\: is \:\: correct}$

$\huge\star\:\:{\orange{\underline{\pink{\mathbf{THANKS!}}}}}$