Question

Sum of areas of two squares is 244 cm² and the difference between their perimeter is 8cm. find the ratio of their diagonal.
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Answer 1

Answer:

Ans is 6:5

Step-by-step explanation:

A to q-:

Sum of areas=244cm^2

Let the side of the squares be a1&a2.

a1^2+a2^2=244------(I)

Difference between perimeter=8cm

=>4a1-4a2=8

=>a1-a2=2

=>a1=2+a2------(ii)

Substituting in eqn (I)

(2+a2)^2+a2^2=244

=>4+(a2)^2+4a2+a2^2=244

=>2(a2)^2+4a2-240=0

=>(a2)^2+2a2-120=0-----(iii)

On solving eqn (iii) a2=10cm

Hence a1=12cm

Therefore, ratio of their diagonals =√2a1/√2a2

=a1/a2=12/10=6/5

Hence the ratio is 6:5.