find the side and parimeter of a square whose diagonal is 10 cm.
Answers
Answer:
Area of square is 50cm^2.
Perimeter of square is 20√2 cm.
Step-by-step explanation:
Let,
Side of this square be a cm.
Given,
Length of diagonal of this square is 10 cm.
Using Pythagoras theorem :
= > side^2 + side^2 = diagonal^2
= > 2 side^2 = diagonal^2
= > 2 side^2 = ( 10 cm )^2
= > 2 side^2 = 100 cm^2
= > side^2 = 50 cm^2 ... ( 1 )
= > side = √{ 50 cm^2 }
= > side = √( 2 x 25 cm^2 )
= > side = 5√2 cm
From the properties of square :
- Area of square : side^2
- Perimeter of square : 4side
Thus,
= > Area of square = ( side )^2
= > Area of square = 50 cm^2 { from ( 1 ) }
= > Perimeter of square = 4 x side = 4 x 5√2 cm = 20√2 cm
Hence area of square is 50cm^2 and perimeter of square is 20√2 cm.
ANSWER : -
Side of the square be x cm.
Length of diagolan of square is 10 cm.
USING PYTHAGORAS THEOREM : -
side² + side² = diagolan²
2 side² = diagonal²
2 side² = (10 cm)²
2 side² = 100 cm²
side² = 50 cm².............(1)
side = √50 cm²
side = √2×5×5
side = 5√2
HENCE,
AREA OF SQUARE = SIDE²= 50 CM²
FROM EQUATION (1)
perimeter of square = 4 × side = 4 × 5√2
= 20√2 cm