The perimeter of one square is 748 cm and that of another is 336 cm. Find the perimeter and the diagonal of a square which is equal in area to these two.
To find the areas of the two squares, solve 4x=748 and 4x=336. The larger square has a side (x) = 187, so the area (x-squared) is 34,969. The smaller square has a side (x) = 84 so the area is 7056. The total area is 42,025. Taking the square root we find that x=205 for the new square. Thus the perimeter (4x) is 820. The diagonal is solved using the pythagorean theorem. The answer is 289.913.
Perimeter of 1st square is 748 cm. So 4 X (one side )=748 cm and we get side=187cm .
And area of this square =187X187=34969 sq. cm
Perimeter of 2nd square is 336 cm. So 4 X (one side)=336 cm and we get side=84cm .And area of this square =84X84=7056 sq. cm
Area of 3rd square is sum the above two squares= 42025 sq. cm.
So, side X side =42025 sq. cm and one side =sq. root of 42025 We get each side as =205 cm . Now perimeter of 3rd square is 4 X 205=820 cm (ANS)
And length of diagonal is (calculated applying the pythagorus theorem ) sq. root of (205X205+205X205) = 289.914 cm (ANS)
Perimeter of the square = 748cm and 336cm
For 1st square
Perimeter of the square =4a
4a=748
a=748/4
a=187 cm
Area
=a^2
=187×187
=34969 sq. cm
For 2nd square
Perimeter of the square =4a
4a=336
a=336/4
a=84 cm
Area
= a^2
=84×84
=7056 sq. cm
If a square is equal in are to these two, then its area is
=34969+7056
=42025 sq. cm
Side of the area
= 42025^1/2
= 205 cm
Perimeter of the new square
=4×205
=820 cm
The diagonal of the new square
= a(2)^(1/2)
= 205 (2)^(1/2)
= 289.914 cm
Answer
Perimeter of the new square = 820 cm^2
Diagonal of the new square = 289.814 cm
