Answer:
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
I would estimate it as (300 x 7) = 2100
Then I would subtract (11 x 7) + 77 from that to get the exact answer of 2023
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I didn't use a calculator or paper. The 'trick' is to notice that 289 = (300 - 11)
The sum of the angles in a pentagon is 540°.
This means that each angle is 108°.
Inside you pentagon, a triangle is drawn. This triangle is isosceles, because the corners are on the points of the regular pentagon. You know that angle C is 108°.
Angles in a triangle add up to 180°.
B and D will be the same size as this is isosceles.
180°-108° = 72°
This is B and D. You only need one of these, so you divide by 2.
The answer is 36°.
Hope this helps :)
