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2 years ago

the diagram shows a 5cm x 5cm x 5cm cube calculate the length of the diagonal AB give your answer correct to 1 decimal place

Mathematics

1 answer:

Lynna [10]2 years ago

4 0

Answer:

√3 * 5 = 5√3 cm

Step-by-step explanation:

→ ABCDEFGH is a cube.

→ CF = Diagonal of cube.

→ CH = Diagonal of Base Face BCDH.

→ Let the 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.)

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2 years ago

12x−39≤9 AND−4x+3<−6, just solving for x please answer ASAP

kari74 [83]

Answer:

Solving for x in 12x − 39 ≤ 9 and −4x + 3 < −6 we get 2.25 < x ≤ 4

Solution:

Need to find the value of x which satisfies following two given expressions

12x − 39 ≤ 9 ------(1)

−4x + 3 < −6 ------ (2)

Lets first solve expression (1)

12x − 39 ≤ 9

Adding 39 on both sides , we get

12x−39 + 39 ≤ 9 +39

=>12x ≤ 48

=> x ≤ 48/12

=> x ≤ 4

Now solving expression (2)

−4x+3<−6

=> -4x < -6 – 3

=> -4x < -9

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=> x > 9/4

=> x > 2.25

So from solution of expression (1) and (2) , we get x ≤ 4 and x > 2.25

Hence required value of x is 2.25 < x ≤ 4.

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