Question

If the side of a square is1/2(x+1) units and its diagonal is(3-x)/√2units, find the length of a side of square.
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Answer 1

Answer:

1 unit

Step-by-step explanation:

Using Pythagoras theorem,

• side^2 + side^2 = diagonal^2

• 2 side^2 = diagonal^2

• √2 side = diagonal

Using the above relation,

=> √2 × 1/2 (x + 1) = (3 - x)/√2

=> √2 × √2 × 1/2 (x + 1) = (3 - x)

=> 2 × 1/2 (x + 1) = 3 - x

=> 1 × (x + 1) = 3 - x

=> x + 1 = 3 - x

=> x + x = 3 - 1

=> 2x = 2

=> x = 1

Therefore,

side of square= 1/2 (x + 1) = 1/2 (1 + 1) =1unit

Answer 2

Given :-

If the side of a square is1/2(x+1) units and its diagonal is(3-x)/√2units,

To Find :-

Length of side

Solution :-

We know that

Diagonal = √2 × side

Diagonal = √2s

Now

√2 × 1/2× (x + 1) = (3 - x)/√2

By cross multiplication

√2 × √2 [1/2 × (x + 1)] = 3 - x

2 × 1/2 × x + 1 = 3 - x

x + 1 = 3 - x

3 - 1 = x + x

2 = 2x

2/2 = x

x = 1

Now

Side of square =  1/2 × (x + 1)

Side = 1/2 × (1 + 1)

Side = 1/2 × 2

Side = 2/2

Side = 1