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galina1969 [7]
3 years ago
10

Explain how you could use the construction tool or a compass and straightedge to create a line segment that is twice as long.

Mathematics
1 answer:
ycow [4]3 years ago
3 0

Answer: Use a compass to measure the length of AB. Draw an arc from point B (or point A) with that distance. Extend line AB through that arc and label the intersection as point C. AC is twice the length of AB.

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Find the
Mazyrski [523]

Answer:

54 cm

Step-by-step explanation:

The area (A) of an equilateral triangle is

A = \frac{s^2\sqrt{3} }{4}  ( s is the side length ) then

\frac{s^2\sqrt{3} }{4} = 81\sqrt{3} ( multiply both sides by 4 to clear the fraction )

s²\sqrt{3} = 324\sqrt{3} ( divide both sides by \sqrt{3} )

s² = 324 ( take the square root of both sides )

s = \sqrt{324} = 18

Thus

perimeter = 3 × 18 = 54 cm

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Step-by-step explanation:

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Estimate the perimeter of the figure to the nearest whole number.
Paha777 [63]

Answer:

The perimeter (to the nearest integer) is 9.

Step-by-step explanation:

The upper half of this figure is a triangle with height 3 and base 6.  If we divide this vertically we get two congruent triangles of height 3 and base 3.  Using the Pythagorean Theorem we find the length of the diagonal of one of these small triangles:  (diagonal)^2 = 3^2 + 3^2, or (diagonal)^2 = 2*3^2.

Therefore the diagonal length is (diagonal) = 3√2, and thus the total length of the uppermost two sides of this figure is 6√2.

The lower half of the figure has the shape of a trapezoid.  Its base is 4.  Both to the left and to the right of the vertical centerline of this trapezoid is a triangle of base 1 and height 3; we need to find the length of the diagonal of one such triangle.  Using the Pythagorean Theorem, we get

(diagonal)^2 = 1^2 + 3^2, or 1 + 9, or 10.  Thus, the length of each diagonal is √10, and so two diagonals comes to 2√10.

Then the perimeter consists of the sum 2√10 + 4 + 6√2.

which, when done on a calculator, comes to 9.48.  We must round this off to the nearest whole number, obtaining the final result 9.

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3 years ago
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