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SVEN [57.7K]
2 years ago
6

What sides are the triangles?

Mathematics
1 answer:
Solnce55 [7]2 years ago
3 0

Answer:

Step-by-step explanation:

From the picture attached,

In ΔABC and ΔGFE,

AC ≅ EG  [Given]

BC ≅ EF [Given]

AB ≅ FG [Given]

By the SSS property of congruence, ΔABC ≅ ΔGFE

The two triangles are related by SSS property of congruence, so the triangles are congruent.

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Please help me AAAAAA
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Answer:

45

Step-by-step explanation:

AEF is a similar triangle to ABC. that means it has the same angles, and the sides (and all other lines in the triangle) are scaled from the ABC length to the AEF length by the same factor f.

now, what is f ?

we know this from the relation of AC to FA.

FA = 12 mm

AC = 12 + 28 = 40 mm

so, going from AC to FA we multiply AC by f so that

AC × f = FA

40 × f = 12

f = 12/40 = 3/10

all other sides, heights, ... if ABC translate to their smaller counterparts in AEF by that multiplication with f (= 3/10).

the area of a triangle is

baseline × height / 2

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and because of the similarity we don't need to calculate the side and height in absolute numbers. we can use the relative sizes by referring to the original dimensions and the scaling factor f.

baseline small = baseline large × f

height small = height large × f

we know that

baseline large × height large / 2 = 500

baseline large × height large = 1000

aAEF = baseline small × height small / 2 =

= baseline large × f × height large × f / 2 =

= baseline large × height large × f² / 2 =

= 1000 × f² / 2 = 500 × f² = 500 ×(3/10)² =

= 500 × 9/100 = 5 × 9 = 45 mm²

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