Three squares are based on the sides of a right angled triangle. The area of the two smaller ones are 144.sq.cm and 256.sq.cm what is the area of the third one
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Given,
The area of the smaller squares are = 144 cm² and 256 cm²
To find,
The area of the third square.
Solution,
The side of first smaller square = ✓144 = 12 cm
The side of second smaller square = ✓256 = 16 cm
So,the length of the two smaller sides of the triangle= 12 cm and 16 cm
Now, the third or the bigger side of the right angle triangle will be the hypotenuse.
Let,the length of the hypotenuse = x cm
According,to the Pythagoras theorem,
x² = (12)² + (16)²
x² = 144 + 256
x² = 400
x = 20
So,the length of one side of the third square = 20 cm
Area of third square = 20×20 = 400 cm²
Hence,the area of the third square is 400 cm².
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