Question

what are the possible expressions for the dimensions of the cuboids whose volumes are given below
a)

$12ky {}^{2} + 8ky - 20k$
​

Answer 1

Explanation:

Volume = 12ky2 + 8ky - 20k

= 4k (3y2 + 2y - 5)

= 4k (3y2 + 5y -3y - 5)

= 4k (y (3y+5) - 1(3y+5))

= 4k (3y +5) (y-1)

Dimensions are l = 4k, b = 3y+5, h = y-1

Answer 2

volume is given by:- 12ky² + 8ky - 20k

to find :- dimension of the cuboid

soln=

volume of cuboid = l×b×h

12ky²+8ky-20k

k(12y²+8y-20)

4k(3y²+2y-5)

4k(3y²+5y-3y-5)

4k(3y(y-1)+5(y-1))

4k((y-1)(3y+5))

length = 4k

breadth = (y-1)

height=(3y+5)