A cuboid with a volume of 924 cm^3 has dimensions 4 cm, (x + 1) cm and (x + 11) cm.
Find the longest length of the Cuboid.

21

Step-by-step explanation:

Volume of a cuboid is given by

V = l*w*h

924 = 4 (x+1) (x+11)

FOIL

924 = 4(x^2 +11x+x+11)

924 = 4(x^2+12x+11)

Divide each side by 4

231 = (x^2+12x+11)

Subtract 231 from each side

0 = x^2 +12x +11-231

0 = x^2 +12x - 220

Factor

0 = (x+22) (x-10)

Using the zero product property

x+22 =0  x-10 =0

x=-22  x=10

We cannot have a negative length

x=10

The side lengths are 4, 10+1, 10+11

4,11,21

The longest is 21

for the first question it would be the second answer for the second question it would be the third answer and for the third question it would be the first answer

step-by-step explanation:

d) by the cross product property, ab^2 = bc multiplied by ad

step-by-step explanation:

we are given

in the given triangle abc

angle a is 90° and segment ad is perpendicular to segment bc

we can see that

triangle(abc) and triangle(abd) are similar because they have common side and same angle (90 degree)

so, triangles(abc) and abd are similar

since, they are similar

so, the ratio of their sides must be equal

we get

now, we can cross multiply

and we get

so, this could be step to prove it