Question

the internal dimensions of a rectangular box are 12 cm *x cm* 9 cmif the length of the longest rod that can be placed in this box is 17 cm find x

Answer 1

simce diagonal=root under (L^2+B^2+h^2)
also,diagonal=17
root under(12^2+x^2+9^2)=17
squaring both sides:
144+x^2+81=289
225+x^2=289
x^2=289-225=64
x=root under 64=8cm

Answer 2

Dear Student,

● Answer -

x = 8 cm

◆ Explanation -

Given that internal dimensions of a rectangular box are 12 cm × x cm × 9 cm.

l = 12 cm

b = x cm

h = 9 cm

Length of the longest rod that can be placed in this box is equal to its diagonal.

Diagonal of rectangular box is given as -

d^2 = l^2 + b^2 + h^2

17^2 = 12^2 + x^2 + 9^2

289 = 144 + 81 + x^2

x^2 = 289 - 144 - 81

x^2 = 64

x = 8 cm

Hence, value of x cm is 8 cm.

Hope this helps you...