Question

The side of a square is 9cm.find the ratio of diagonal of a square to its side
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Answer 1

Step-by-step explanation:

The diagonal and two adjacent sides of the square form an isosceles right triangle.

Recall from trigonometry that the reference isosceles right triangle has hypotenuse equal to 1 and its two legs each have length 2√ 2.

Since all plane isosceles right triangles are similar, multiply the lengths of the sides and the length of the hypotenuse of the reference triangle by 9. The resulting triangle has a diagonal of length 9.

∴ the length of a side of the given square is

92–√2 cm.

2.) Another way is to let s be the length of a side of the square. Again, the 9-cm diagonal and two adjacent sides form an isosceles right triangle.

By the Pythagorean theorem

s2+s2=(9 cm)2

⟹2s2=81 cm2

⟹s2=812 cm2

⟹s2−−√=812 cm2−−−−−−√

⟹s=81−−√2–√cm2−−−√

= 92–√ cm.