Tag: length of the diagonal of cube

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Questions Related to length of the diagonal of cube

Multiple choice maths surface area and volume of cube and cuboid finding out the diagonal of cube and cuboid length of the diagonal of cube diagonal of cube and cuboid

Are all of the following triplets are pythagorean?
$(8,\,15,\,17)$
$(16,\,63,\,65)$
$12,\,16,\,20$

  1. Yes

  2. No

  3. Cannot be determined

  4. None
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

To check if the set of numbers $ {a,b,c} $are Pythagorean triplets, we need to check if $ {a}^{2} + {b}^{2} = {c}^{2} $

1) For $ {8,15,17} $
$ {8}^{2} + {15}^{2} = 64 + 225 = 289 $
and $ {17}^{2} = 289 $
Hence, $ {8}^{2} + {15}^{2} = {17}^{2} $

2) For $ {16,63,65} $
$ {16}^{2} + {63}^{2} = 256 + 3969 = 4225 $
and $ {65}^{2} = 4225 $
Hence, $ {16}^{2} + {63}^{2} = {65}^{2} $

3)For $ {12,16,20} $
$ {12}^{2} + {16}^{2} = 144 + 256 = 400 $
and $ {20}^{2} = 400 $
Hence, $ {12}^{2} + {16}^{2} = {20}^{2} $

Thus, the given set of numbers are Pythagorean triplets.

Multiple choice maths surface area and volume of cube and cuboid finding out the diagonal of cube and cuboid length of the diagonal of cube diagonal of cube and cuboid

Write the Pythagorean triplet whose one member is 30.

  1. $226$ and $224$
  2. $220$ and $222$
  3. $227$ and $229$

  4. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Solution:

General form of pythagorean triplets are $m^2-1,2m,m^2+1$

$\Rightarrow$First member of triplet $a=2m=30\Rightarrow m=15$


Since, it is even 
$\Rightarrow$So, second member of triplet $b=\left(m\right)^2-1=15^2-1=225-1=224$

$\Rightarrow$And third member of triplet $c=m^2+1=225+1=226$

Hence, $A$ is the correct option.

Multiple choice maths surface area and volume of cube and cuboid finding out the diagonal of cube and cuboid length of the diagonal of cube diagonal of cube and cuboid

Find the pythagorean triplet.

  1. $12,35,37$
  2. $12,36,37$
  3. $12,43,47$

  4. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Every right triangle has side length satisfying:

a$^{2}$ $+$ b$^{2}$ $=$ c$^{2}$
c is the longest side,
Here 
$12^{2}$ $+$ $35^{2}$ $=$ $37^{2}$
Hence it is a pythagorean triplet.
Option A is correct.

Multiple choice maths surface area and volume of cube and cuboid finding out the diagonal of cube and cuboid length of the diagonal of cube diagonal of cube and cuboid

A lady went for a walk and she was walking in a right triangular park. The tiles of the smallest side were visible while other 2 sides she couldn't make out. Each tile was 1 m. The length of the visible side was 10 m. Help the lady to find the length of the other 2 sides , so she could calculate what distance she is walking everyday. 

  1. 14 m and 16 m

  2. 22 m and 23 m

  3. 24 m and 26 m

  4. 42 m and 46 m
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

one side$=10 m$

Other two sides and 10 m should be Pythagorean triplet in order to form right triangle.
$14^{2}$$+$$10^{2}$$=$$296$
$22^{2}$$+$$10^{2}$$=$$584$

$24^{2}$$+$$10^{2}$$=$$576$
$576$$=$$26^{2}$
$42^{2}$$+$$10^{2}$$=$$1864$
Hence, Option C is correct.

Multiple choice maths surface area and volume of cube and cuboid finding out the diagonal of cube and cuboid length of the diagonal of cube diagonal of cube and cuboid

Find the pythagorean triplet.

  1. $8, 15, 17$
  2. $9, 10, 15$
  3. $9, 10, 17$

  4. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Every right triangle has side length satisfying:

a$^{2}$ $+$ b$^{2}$ $=$ c$^{2}$
c is the longest side,
Here 
$8^{2}$ $+$ $15^{2}$ $=$ $17^{2}$
Hence it is a pythagorean triplet.
Option A is correct.

Multiple choice maths surface area and volume of cube and cuboid finding out the diagonal of cube and cuboid length of the diagonal of cube diagonal of cube and cuboid

Write the Pythagorean triplet whose one member is $24$.

  1. $143$ and $145$
  2. $133$ and $144$
  3. $112$ and $115$
  4. $324$ and $325$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Using  $ 2m, m^2+1, m^2-1$ forms

 Let us take $2m = 24$

$m=\dfrac{24}{2}=12$

if $m = 12, m^2-1=12^2= 144-1 =143$

if $ m = 12, m^2 +1=12^2= 144+1 =145$

Therefore, option A is the correct answer.

Multiple choice maths surface area and volume of cube and cuboid finding out the diagonal of cube and cuboid length of the diagonal of cube diagonal of cube and cuboid

Find the Pythagorean triplet whose one member is $18$.

  1. $28$ and $20$
  2. $80$ and $82$
  3. $72$ and $92$
  4. $34$ and $54$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Using  $ 2m, m^2+1, m^2-1$ forms 
Let us take $2m = 18$
           

$m=\dfrac{18}{2}=9$
if $m = 9, m^2-1=9^2= 81-1 =80$
if $ m = 9, m^2 +1=9^2= 81+1 =82$
Therefore, B is the correct answer.

Multiple choice maths surface area and volume of cube and cuboid finding out the diagonal of cube and cuboid length of the diagonal of cube diagonal of cube and cuboid

What is the value of x, if (7, x, x - 2) is a Pythagorean triple?

  1. -11.25

  2. 26.5

  3. -16.5

  4. 16.5
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Applying the Pythagorean triples rule as $a^{2}+b^{2}= c^{2}$
$7^{2}+x^{2}= (x - 2)^{2}$
49 + $x^{2}$ = $x^{2}$+ 4 -4x
Both the side $x^{2}$ will get cancelled,
45 = -4x
x = -11.25