Answer:
One rectangular prism is possible with 7cm × 3cm × 4cm.
Step-by-step explanation:
Jada used number of cubes = 84
Side of one small cube = 1 cm
Volume of one small cube = 1 cm³
Volume of 84 small cubes = 84 cm³
She wants to build a rectangular prism with height = 4 cm
Let the length of the prism = x cm
and the width of the prism = y cm
and x > y
Volume of the prism = length × width × height
= (x)(y)(4)
= 4xy cm³
If the volume of prism = volume of 84 small cubes
Then 4xy = 84
xy = 21
Possible values of x = 3, 7
and y = 7, 3
But x > y
So x = 7 and y = 3 will be the answer.
Therefore, only one rectangular prism is possible with dimensions
length = 7 cm, width = 3 cm, height = 4 cm.
5÷3 or 5/3 I hope that helps u
Answer:
b = sqrt(39)
Step-by-step explanation:
Since this is a right triangle, we can use the Pythagorean theorem
a^2+b^2 = c^2
5^2 + b^2 = 8^2
25+b^2 =64
b^2 =64-25
b^2 =39
Take the square root of each side
b = sqrt(39)
Answer:
8,5
Step-by-step explanation:
a=b+3
(b+3+b)*2=26
b=5
a=8
<h3>
Answer: b) 18 cm </h3>
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Work Shown:
Since the parallelogram has perpendicular diagonals, this means that we're dealing with a rhombus. A rhombus has all four sides equal to one another.
One diagonal is bisected, or cut in half, to form the smaller pieces of length (150/x) + 10 and x-10. Set these two expressions equal to each other and solve for x
(150/x) + 10 = x-10
1500/x = x-10-10
1500/x = x-20
1500 = x(x-20)
1500 = x^2-20x
0 = x^2-20x-1500
x^2-20x-1500 = 0
(x-50)(x+30) = 0
x-50 = 0 or x+30 = 0
x = 50 or x = -30
We'll ignore the negative x value as it leads to a negative length which doesn't make sense.
If x = 50, then
- x-10 = 50-10 = 40
- (150/x)+10 = (150/50)+10 = 30+10 = 40
Each piece of this diagonal is 40 cm long.
The two smaller pieces combine to 40+40 = 80, which is the length of one of the diagonals. If this was the shorter diagonal, then 80 would be listed as part of the answer choices. However, 80 is not one of the answers.
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Note how the two diagonals of the rhombus cut the figure into four right triangles.
Each right triangle has one known leg to be 40 and an unknown leg of y. The hypotenuse is 164/4 = 41 since we divide the perimeter by the four equal sides of the rhombus.
We'll use the pythagorean theorem to find the value of y
a^2 + b^2 = c^2
40^2 + y^2 = 41^2
1600 + y^2 = 1681
y^2 = 1681-1600
y^2 = 81
y = sqrt(81)
y = 9
This represents half of the other diagonal, so the full length of this other diagonal is 2*9 = 18 cm.
