similar triangles have the same angles, and all side lengths (or other distances) of one triangle have the same scaling factor to the side lengths of the other triangle.

so, we know the relation between the 2 baselines is 2/3, as this is the factor to turn the baseline of the large triangle into the baseline of the smaller triangle.

in other words

EF = BC × 2/3

2 = 3 × 2/3

correct

how do we calculate the area of a triangle ?

Area = baseline × height / 2

from BAC we know

Area = 6

baseline = 3

height = ?

6 = 3 × height / 2

12 = 3 × height

height = 4

aha !

now, EDF has a height too that we need to calculate is Area. and this height has the same scaling factor compared to the larger triangle as the side lengths : 2/3

so, for EDF we know

Area = ?

baseline = 2

height = 4 × 2/3 = 8/3

therefore, the area is

Area = (2 × 8/3) / 2 = (16/3) / 2 = 8/3 = 2.66666... ≈ 2.7

the shirt answer would be :

we know from the 2 baselines that the scaling factor for each distance is 2/3.

for the area we need to multiply 2 distances, so that means we have to multiply both by 2/3. and so on the formula for the area we have to use 2/3 × 2/3.

2/3 × 2/3 = 4/9

Area small = Area large × 4/9 = 6 × 4/9 = 24/9 = 8/3 ≈ 2.7

3 0

2 years ago

The points (–2, 4) and (–2, –2) are vertices of a heptagon. Explain how to find the length of the segment formed by these endpoi

Scrat [10]

Answer:

The segment is 6 units long.

Step-by-step explanation:

The points (–2, 4) and (–2, –2) are vertices of a heptagon. We have to explain how to find the length of the segment formed by these endpoints.

If two points at the ends of a straight line PQ are P( $x_{1},y_{1}$ ) and Q( $x_{2},y_{2}$ ), then the length of the segment PQ will be given by the formula

$\sqrt{(x_{1} - x_{2})^{2} + (y_{1} - y_{2})^{2}}$

Now, in our case the two points are (-2,4) and (-2,-2) and the length of the segment will be

$\sqrt{(- 2 - (- 2))^{2} + (4 - (- 2))^{2}} = 6$ units. (Answer)

5 0

3 years ago

Read 2 more answers

Translate the expression into a word phrase. k + 12 A. a number less than 12 B. 12 more than a number C. the product of a number

Burka [1]

The answer is b) 12 more than a number

when you use the word "more than" it means addition. when you use the word "less than" it means subtraction. when you use the word "product of" it means multiplication. when you use "quotient of" it mean division.

hope that helps, God bless! <span />

8 0

3 years ago