Find possible expressions for the length, breadth, and heights of each of the following cuboids Class 9

Find possible expressions for the length, breadth, and heights of each of the following cuboids Class 9

Question 1.

Find possible expressions for the length, breadth, and heights of each of the following cuboids whose volumes are given by the following expressions in cubic units.

i. 6a² - 24b²

ii. 3ps² - 15ps + 12p

Solution:

i. Given, volume = 6a² - 24b²

= 6(a² - 4b²)

= 6[² - (2b)²]

= 6(a - 2b)(a + 2b)

...[∵ A² - B² = (A + B)(A - B)]

Since volume of cuboid

= length × breadth × height,

possible length = 6,

possible breadth = a - 2b,

possible height = a + 2b

[Note: There are multiple possible solutions. This is one possible set of dimensions.]

ii. Given, volume = 3ps² - 15ps + 12p

= 3p(s² - 5s + 4)

s² - 5s + 4

Since (-1) + (-4) = -5 and (-1) × (-4) = 4,

the numbers are -1 and -4.

s² - 5s + 4 = (s - 1)(s - 4)

∴ Volume = 3p(s - 1)(s - 4)

Since volume of cuboid

= length × breadth × height,

possible length = 3p,

possible breadth = s - 1,

possible height = s - 4

[Note: There are multiple possible solutions. This is one possible set of dimensions.]