Question

The length of the side of a square is 45cm. what is the length of the diagonal of square whose area is 1/9th of the original square?

Answer 1

Answer:

21.21 cm

Step-by-step explanation:

First, Area of given square = a^2 = side × side = side^2 (all formula, just for knowledge)

Here, 【Original sq】

Area of ◻ = (45cm)^2= (45 × 45) cm sq ..... (1)

= 2025 cm sq ....(2)

Again,

Area of new sq = 1/9 th of Original .....(3)

So, from (1) &(3)

Area = (1/9) × 45 × 45 = 45/9 × 45 = 5 × 45= 225 cm sq

➡➡➡➡ OR (any way u can do...)

AREA = 1/9* 2025 = 2025/9 = 225 CM Sq ....(4)

Now, from (4)

Side of new Sq = √225 = 15 cm .....(5)

Based on (5) apply Pythagorean property,

Diagonal of new Sq, (Let, D)

D = √[15^2 + 15^2] cm

D= √450 = 21.21 cm (approx)