Question

diagonal of square is 42 cm the diagonal of another square who area is double that of the first sqare is

Answer 1

First, giving names to both the squares,
• the square which have a diagonal of length 42cm is ABCD.
• the square who has the area twice of square ABCD is PQRS.

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In ABCD,

As we know that, in square all sides are perpendicular to each other,

By Pythagoras theorem,

(Side)² + (side)² = (diagonal)²

2(side)² = 42²

2(side)² = 1764

Side² = 1764/2

Side² = 882

Side= √882 cm

Area of ABCD = side²

Area of ABCD = (√882)²

Area of ABCD = 882 cm²

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Then,

In PQRS,

According to the question,

Area of PQRS =2×area of ABCD

Area of PQRS = 2×882

Area of PQRS = 1764

Side² = 1764

side = 42 cm

Now,

By Pythagoras theorem,

side² + side² = diagonal²

42²+42² = diagonal²

1764+1764 = diagonal²

3528= diagonal²

√3528= diagonal

I hope this will help you

-by ABHAY