Question

there square are based on the sides of a right angle triangle the area of the two smaller one are 144sq. cm and 256sq .cm . what is the area of the third one.​

Answer 1

Answer:

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.

Step-by-step explanation:

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