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The two quadrilaterals are given similar .
In any similar figure sides are in proportion.The second largest side of quadrilateral ABCD is 16 ft .Let the second longest side of quadrilateral EFGH be x ft. These sides will be in proportion to each other .
The second shortest side of quadrilateral EFGH that is GF will be proportional to the third longest side of quadrilateral ABCD that is BC
We can form a proportion with the proportional sides:
To solve for x we cross multiply
12x=(16)(18)
12x=288
Dividing both sides by 12 we get
x=24.
The second longest side of quadrilateral EFGH is 24 ft.
Answer:
a. (30 - 2x)(16 - 2x)x. b. length 21.2 cm , width = 7.2 cm and height x = 4.4 cm
Step-by-step explanation:
a. Let x be the side of the squares to be cut from each corner. Since we have two corners on each side, the length of the resulting box from the 30 cm by 16 cm sheet is L = 30 - 2x. Its breadth is B = 16 - 2x. The height of the resulting box is x. So its volume V = LBx = (30 - 2x)(16 - 2x)x.
b. To find the maximum value of V, we differentiate V with respect to x and equate it to zero.
So, dV/dx = 0
d(30 - 2x)(16 - 2x)x/dx = 0
-2(16 - 2x)x + (-2)(30 - 2x)x + (30 - 2x)(16 - 2x) = 0
32x + 4x² - 60x - 4x² + 480 - 60x - 32x + 4x² = 0
4x²- 120x + 450 = 0
x²- 30x + 112.5 = 0
Using the quadratic formula, we find x. So, with a = 1, b = - 15 and c = 112.5,
x ≅ 25.61 or 4.4
V = (30 - 2x)(16 - 2x)x
Substituting the values of x into L and B, we have )x
L = (30 - 2x) = (30 - 2(25.61)) = 30 - 51.22 = -21.22
B = (16 - 2x) = (16 - 2(25.61)) = 16 - 51.22 = -35.22
Since L and B cannot be negative, we use the other value for x = 4.4, So
L = (30 - 2x) = (30 - 2(4.4)) = 30 - 8.8 = 21.2
B = (16 - 2x) = (16 - 2(4.4)) = 16 - 8.8 = 7.2
So V = LBx = 21.2 × 7.2 × 4.4 = 671.62 cm³