Question

classmate
Date
ond &
Sum of
areas of two squares is 249 en
the difference between their perimeter is 8 cm
Find the
of their diagonals.
ratio​

Answer 1

Step-by-step explanation:

Let the side length of two squares be x and y respectively.

Given, Perimeter difference = 8

So

\begin{gathered}4x - 4y = 8 \\ x - y = 2 \\ x = y + 2 - - - (1)\end{gathered}

4x−4y=8

x−y=2

x=y+2−−−(1)

Sum of areas = 244

So

\begin{gathered} {x}^{2} + {y}^{2} = 244 \\ substituting \: \: from \: \: (1) \\ {(y + 2)}^{2} + {y}^{2} = 244 \\ {y}^{2} + 2y - 120 = 0 \\ (y + 12)(y - 10) = 0 \\ considering \: \: positive \: \: value \: \\ y = 10 \\ from \: \: (1) \\ x = 10 + 2 = 12 \\ \\ ratio \: \: of \: \: diagonals = \sqrt{2} x : \sqrt{2} y \\ = x:y = 12:10 = 6:5\end{gathered}

x

2

+y

2

=244

substitutingfrom(1)

(y+2)

2

+y

2

=244

y

2

+2y−120=0

(y+12)(y−10)=0

consideringpositivevalue

y=10

from(1)

x=10+2=12

ratioofdiagonals=

2

x:

2

y

=x:y=12:10=6:5