Question

the diagonals of a square are in ratio 5:2.the ratio of their area is
a]5:6
b] 5:4
c] 25:4
d] 125:8

Answer 1

Given :-

• Diagonals of 2 Square are = 5 : 2.

To Find :-

• Ratio of Their Area = ? .

Formula used :-

• Area of Square when Diagonal is Given = (Diagonal)² / 2

Solution :-

Let Diagonals of Both Square are 5x & 2x Respectively.

So,

→ Area of First Square = (5x)² / 2 = (25x²/2)

And ,

→ Area of Second Square = (2x)²/2 = (4x²/2).

Therefore,

→ Ratio of Area of Both Square = (25x²/2) : (4x²/2) = 25 : 4.

Hence, Ratio of Area of Both Square is 25 : 4. (Option C).

Answer 2

Solution:

Let the diagonals of square be 5x and 2x.

We know that,

Area of Square = (Diagonal)²/2

Now,

Area of 1st square = (Diagonal)²/2

= (5x)²/2

=25x²/2

Area of 2nd square = (Diagonal)²/2

=(2x)²/2

=4x²/2

Ratio of their area = 25x²/2 : 4x²/2

= 25 : 4

Extra:

• Area of rectangle = length × breadth
• Area of parallelogram = Base × Altitude
• Area of triangle = 1/2 × Base × height