A square ABCD is of side 5 cm. find the length of its diagonal
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Answered by
9
Step-by-step explanation:
STEP BY STEP EXPLANATION:
Given: ABCD is a square with side 5cm.
To find: AC
We know that all the sides of square are equal,
so,AB=BC=CD=DA=5cm
We know that all the angles of square are 90°.
So by Pythagorean theorem,
(Hypotenuse)²=(Perpendicular)²+(Base)²
(AC)²=(BC)²+(AB)²
(AC)²=(5)²+(5)²
(AC)²=(25+25)cm
(AC)²=50cm
AC=√50cm
AC=7.07cm
HENCE,PROVED.
Answered by
5
A square ABCD is of side 5 cm. find the length of its diagonal
side = 5 cm
diagonal = AC
By Pythagoras theorem,
(AC)² = (AB)² + (BC)²
(AC)² = (5)² + (5)²
(AC)² = 25 + 25
(AC)² = 50
AC = √50
AC = √2 × 5 × 5
AC = 5√2 cm
OR
diagonal = √2 × side
= 5√2 cm
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