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Flura [38]
2 years ago
12

ΔABC is similar to ΔDEF. The ratio of the perimeter of ΔABC to the perimeter of ΔDEF is 1 : 5. If the longest side of ΔDEF measu

res 15 units, what is the length of the longest side of ΔABC?
Mathematics
1 answer:
PilotLPTM [1.2K]2 years ago
8 0

Answer:

Length of the longest side of ΔABC = 3 units

Step-by-step explanation:

If two similar triangles have a scale factor a:b, then the ratio of perimeters is also a:b.

Here, the converse is applied.

The perimeter of similar triangles is in the ratio 1:5, so, the corresponding lengths are also in the ratio 1:5

Perimeter of ΔABC : Perimeter of ΔDEF = 1:5

Longest side of ΔABC : Longest side of ΔDEF = 1:5

Longest side of ΔABC : 15 = 1:5

∴ Longest side of ΔABC = (1/5) * 15 = 3 units

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Answer:

Step-by-step explanation:

4). a). If the diagonals of a parallelogram are congruent, then it must be a RECTANGLE.

b). If the diagonals of a parallelogram are perpendicular, then it must be a SQUARE.

c). If the diagonals of a parallelogram bisect the angles of the parallelogram, then it must be a RHOMBUS.

d). If the diagonals of a parallelogram are perpendicular and congruent, then it must be a SQUARE.

e). If a parallelogram has four congruent sides, then it must be a SQUARE.

5). Given quadrilateral SELF is a rhombus.

a). All sides of a rhombus are equal,

   Therefore, ES = EL = 25

b). Diagonals of a rhombus bisects the opposite angles,

   Therefore, m∠ELS = m∠FLS

    3x - 2 = 2x + 7

    3x - 2x = 7 + 2

    x = 9

c). Diagonals of the rhombus bisect the opposite angles, and adjacent angles are supplementary.

m∠ELF = 2(m∠ELS) = 2(2y - 9)

m∠LES = 2(m∠LEF) = 2(3y + 9)

And 2(2y - 9) + 2(3y + 9) = 180

(2y - 9) + (3y + 9) = 90

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3 years ago
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AleksandrR [38]

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2 years ago
List down 5 values of x that makes it TRUE to the equation x - 5 < 35
Molodets [167]

Answer:

5,4,3,2,1

Step-by-step explanation:

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3 years ago
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Marysya12 [62]

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Step-by-step explanation:

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3 years ago
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lys-0071 [83]

Answer:

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Step-by-step explanation:

According to Hooke's law which states that extension of an elastic material is directly proportional to the applied force provide that the elastic limit is not exceeded. Mathematically,

F = ke where

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e is the extension

If a spring exerts a force of 6 N when stretched 3 m beyond its natural length, its elastic constant 'k'

can be gotten using k = f/e where

F = 6N, e = 3m

K = 6N/3m

K = 2N/m

Work done on an elastic string is calculated using 1/2ke².

If the spring is stretched 2 m beyond its natural length, the work done on the spring will be;

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