Question

The diagram shows a 5cm x 5cm x 5cm cube calculate the length of the diagonal ab

Answer 1

Solution :-

Refer to Image first .

From image we have :-

→ ABCDEFGH is a cube.

→ CF = Diagonal of cube.

→ CH = Diagonal of Base Face BCDH .

→ Let side of Each cube = a .

Than ,

in Right ∆CFH, By Pythagoras Theoram , we have,

→ CH² + FH² = CF² --------- Equation (1)

and, Similarly, in Right ∆CDH ,

→ CD² + DH² = CH² ------- Equation (2).

Putting Value of Equation (2) in Equation (1) , we get,

→ (CD² + DH²) + FH² = CF²

→ a² + a² + a² = CF²

→ CF² = 3a²

→ CF = √3a .

Hence, we can say That, Diagonal of a cube is √3 times of its sides.

__________________

Given :-

• Side of cube = 5cm.

So,

→ Diagonal of cube = √3 * 5 = 5√3 cm. (Ans.)

___________________

Answer 2

$\setlength{\unitlength}{0.74 cm}\begin{picture}(12,4)\thicklines\put(5.6,5.6){ A }\put(11.1,5.8){ B }\put(11.08,8.9){ C }\put(5.46,8.7){ D }\put(3.55,10.15){ E }\put(3.55,7.15){ F }\put(9.14,10.235){ H }\put(9.14,7.3){ G }\put(3.3,6.3){}\put(7.75,6.2){}\put(11.1,7.5){}\put(6,6){\line(1,0){5}}\put(6,9){\line(1,0){5}}\put(11,9){\line(0,-1){3}}\put(6,6){\line(0,1){3}}\put(4,7.3){\line(1,0){5}}\put(4,10.3){\line(1,0){5}}\put(9,10.3){\line(0,-1){3}}\put(4,7.3){\line(0,1){3}}\put(6,6){\line(-3,2){2}}\put(6,9){\line(-3,2){2}}\put(11,9){\line(-3,2){2}}\put(11,6){\line(-3,2){2}}\end{picture}$

$\rule{200}3$

Solution :-

Refer to Image first .

From image we have :-

→ ABCDEFGH is a cube.

→ CF = Diagonal of cube.

→ CH = Diagonal of Base Face BCDH .

→ Let side of Each cube = a .

Than ,

in Right ∆CFH, By Pythagoras Theoram , we have,

→ CH² + FH² = CF² --------- Equation (1)

and, Similarly, in Right ∆CDH ,

→ CD² + DH² = CH² ------- Equation (2).

Putting Value of Equation (2) in Equation (1) , we get,

→ (CD² + DH²) + FH² = CF²

→ a² + a² + a² = CF²

→ CF² = 3a²

→ CF = √3a .

Hence, we can say That, Diagonal of a cube is √3 times of its sides.

__________________

Given :-

Side of cube = 5cm.

So,

→ Diagonal of cube = √3 * 5 = 5√3 cm. (Ans.)

___________________