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Answer = 55,25 inches
Solution -
let's take x as length and y as width of the metal piece. As per the question x is 30 more than y,
⇒ x = y + 30
Then four square pieces of side 6 are cut from each corner,
so the new length and width are
x-12 , y-12
Then the volume of the new box created will be
(x-12)(y-12)6
in the question the volume of the given figure is given to be 3354
so (x-12)(y-12)6 = 3354
putting the value of x in the the above equation
⇒ (y+30 - 12)(x-12) = 3354/6 = 559
⇒ (y+18)(y-12) = 559
⇒ y² + 6y - 775 = 0
⇒ y² + 31y - 25y -775 = 0
⇒ (y+31)(y-25) = 0
⇒ y = -31, 25
as length can not be -ve , so y = 25
then x = 25+30 = 55
Hence the dimensions of the metal piece are 55, 25 inches
Answer:
1 6 15 20 15 6 1
Step-by-step explanation:
To figure this out, we need to look at Pascal's Triangle, which is a tricky little way to find the coefficients for any binomial expression like this! Check the attached photo.
Because this is to the sixth, we need the 6th row, which is <u>1 6 15 20 15 6 1.</u> From this, we know that those numbers are the coefficients!
*see attachment for the figure described
Answer:
5 units
Step-by-step explanation:
==>Given the figure attached below, let where FH and EG intercepted be K.
Since FH are midpoints of parallel lines, KE = KG = x.
Given that the area of the kite EFGH = 35 square units, and we know the length of one of the diagonals = HF = KF + KH = 2 + 5 = 7, we can solve for x using the formula for the area of a kite.
Area of kite = ½ × d1 × d2
Where d1 = KH = 7
d2 = EG = KE + KG = x + x = 2x
Area of kite EFGH = 35
THUS:
35 = ½ × 7 × 2x
35 = 1 × 7 × x
35 = 7x
Divide both sides by 7
35/7 = x
x = 5
