Question

three squares are based on the sides of a right angle triangla. the area of the two smaller ones are 144sq.cm and 256sq.cm. what is the area of the third one?​

Answer 1

$\large\frak{\underline{\underline{\pink{Given :-}}}}$

• Area of the first square = 144² cm
• Area of the second square =  256² cm.  

$\large\frak{\underline{\underline{\pink{To\:Find :-}}}}$

• Area of the third square.

$\large\frak{\underline{\underline{\pink{Solution :-}}}}$

• Side of first square = √144 = 12 cm

• Side of second square = √256 = 16 cm

So,

• Length of the two smaller sides of the triangle = 12 cm and 16 cm

Now,

☯ Third side of the right angle triangle will be the hypotenuse.

Let the length of the hypotenuse be x cm

According to the Pythagoras theorem :

→ x² = (12)² + (16)²

→ x² = 144 + 256

→ x² = 400

→ x = 20

So,

Length of one side of the third square = 20 cm

Area of third square = 20×20

                                  = 400 cm²

∴ The area of the third square = 400 cm².

Answer 2

• Side of first square = √144 = 12 cm
• Side of second square = √256 = 16 cm

So,

• Length of the two smaller sides of the triangle = 12 cm and 16 cm

Now,

• ☯ Third side of the right angle triangle will be the hypotenuse.

Let the length of the hypotenuse be x cm

According to the Pythagoras theorem :

x² = (12)² + (16)²

→ x² = 144 + 256

→ x² = 400

→ x = 20

So,

• Length of one side of the third square = 20 cm

• Area of third square = 20×20

= 400 cm²

• ∴ The area of the third square = 400 cm².

Mark ❤️