In this diagram, ABAC – AEDF. If the area of ABAC = 6 in?, what is the area of AEDF?

Mathematics

1 answer:

shepuryov [24]2 years ago

3 0

Answer:

2.7 in²

Step-by-step explanation:

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

You might be interested in

I need help on 1/2/3/4

vaieri [72.5K]

You may need to sit down with your parents or with your teacher and
go over how to add and subtract fractions.

1). "Perimeter" means the distance all the way around the square.
With a square, all 4 sides are the same length. With this square,
every side is 1-1/4 inches long.

Perimeter = length of all 4 sides= (1-1/4) + (1-1/4) + (1-1/4) + (1-1/4) =

 (1 + 1 + 1 + 1) + (1/4 + 1/4 + 1/4 + 1/4) =

 4 + 4/4 = 5 inches .

2). (2-3/8) + (1-7/8) = (2 + 1) + (3/8 + 7/8) =

 (3) + (10/8) =

 3 + 1-1/4 = 4-1/4 .

3). The difference is (1-1/6) minus (5/6) .

Before you start to do the subtraction, write the (1-1/6) as (7/6) .

Then the subtraction is (7/6) - (5/6) = 2/6 = 1/3 .

4). This one is almost the same kind of problem as #3.
It's another subtraction.

If you need (2-1/4) all together, and you already have (1-3/8),
then the amount you still have to find, or borrow, or buy, is the
difference between those two numbers.

 (2-1/4) minus (1-3/8) .

The trick is to write the (2-1/4) in some form that you'll be able to
subtract (1-3/8) from it. When I learned how to do that, it was called
'borrowing', but I think now it's called 'regrouping'.

We need to work on (2-1/4):

-- take 1 from the 2, and change it into fourths.

 2-1/4 = 1 and 4/4 and 1/4 = 1 and 5/4

-- Now, take those 5/4, and turn them into eighths.
 Each fourth makes 2 eighths. So 5/4 = 10/8.

Now, the (2-1/4) has turned into 1-10/8 .
We did NOT change the value. It's still the same amount
as 2-1/4 , but it's just written in a different way.
And now the subtraction is easy:

 (2-1/4) minus (1-3/8) =

 (1-10/8) minus (1-3/8) = (zero and 7/8).

You need 7/8 inch more string than you already have.

5 0

3 years ago

When writing a linear equation in standard form, what other forms might you need to use?

wlad13 [49]

Answer:

there are 2 other forms, point-slope form and slope-intercept form.

Step-by-step explanation:

standard is $Ax + By =C$