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2 answers:
Answer:
Step-by-step explanation:
The area of the figure consists of a rectangle with a triangle removed from the corner of it. Therefore, the area of the composite of the figure can be found by subtracting the area of the triangle from the area of the rectangle.
Area of the rectangle:
Area of the triangle:
Thus, the area of the figure is
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Answer:
The dimension of the box is 18.66 in by 2.66 in by 1.17 in.
Step-by-step explanation:
Given that, The cardboard is 21 in. long and 5 in. wide.
Assume,x be the length of the each sides of the square .
Then the length of the box is = (21-2x) in.
The breadth of the box is =(5-2x) in.
The height of the box is = length of side of the square
= x in.
The volume of the box = length × wide × height
=(21-2x)(5-2x)x
=(105-52x+4x²)x
=()
Let
V=
Differentiating with respect to x
Again differentiating with respect to x
To find the dimension of the box, we set V'=0
Applying the quadratic formula , here a=12, b= -104 and c =105
=7.5, 1.17
For x= 7.5 , the wide of the box will be negative.
∴x=1.17 in.
Since at x= 1.17, V''<0 , therefore at x=1.17 in. the volume of the given box will be maximum.
The length of the box is = [21-(1.17×2)]=18.66 in.
The wide of the box is = [5-(1.17×2)]=2.66 in.
The height of the box is = 1.17 in.
The dimension of the box is 18.66 in by 2.66 in by 1.17 in.