Question

The area of rhombus of side 8cm and height 8cm is same as the area of square . The side of the square is _?

Answer 1

area of rhombus=base *height
=8*8=64cm2
then,
area of square =side x side
=64cm2
the side of square =√64
=8cm

Answer 2

We know by the Pythagorean theorem that a2+b2=c2a2+b2=c2. We also know that the diagonal of a square is the hypotenuse of an isosceles triangle. Using this information we compute the side-length of the square:

a^2 + a^2 = 82

⇒2a^2=64⇒2a^2=64

⇒a^2=32⇒a^2=32

⇒a=root32
a=4root2

Thus the side-length of the square is 42–√42cm. The area of a square is given by the following formula:

A=s^2

where A is the area and s is the side-length. Thus,

A=(4r2oot)^2

⇒A=16⋅2

⇒A=32cm2
The length of the side is 8 cm.