Question

The diagonal of a square and that of rectangle with length 1.2 cm and breath 0.8 cm are equal. Find the side of the square correct to two decimal places.

Answer 1

Answer:

1.02 cm

Step-by-step explanation:

Let ABCD be the square and EFGH be the rectangle.

Then,

EH = FG = 1.2 cm

HG = EF = 0.8 cm

In right-∆EGH, by Pythagoras Theorem,

EG² = EH² + HG²

= (1.2 cm)² + (0.8 cm)²

= 1.44 cm² + 0.64 cm²

= 2.08 cm²

EG = √2.08 cm

As the diagonal of a square and that of rectangle are equal,

EG = AC = √2.08 cm

Now, in right-∆ABC, by Pythagoras Theorem,

AB² + BC² = AC²

AB² + AB² = (√2.08 cm)² [AB=BC as sides of a square are equal]

or, 2AB² = 2.08 cm²

or, AB² = 1.04 cm²

So, AB = √1.04 cm ≈ 1.02 cm

Hence, the side of the square is 1.02 cm (approximately).

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