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3 years ago

Given that B, D and F are midpoints, find the length of segment DA.

Mathematics

2 answers:

TiliK225 [7]3 years ago

6 0

Answer:

The length of segment DA is 15 units

Step-by-step explanation:

The segment which joining a vertex of a triangle and the midpoint of the opposite side to this vertex is called a median

The point of intersection of the median of a triangle divides each median into two parts the ratio between them is 1: 2 from the base, which means the length of the median is 3 times the part from the base

Let us use this rule to solve the question

In Δ AEC

∵ D is the midpoint of EC

∴ AD is a median

∵ B is the midpoint of AC

∴ EB is a median

∵ F is the midpoint of AE

∴ CF is a median

→ The three medians intersected at a point inside the triangle,

let us called it M

∵ AD ∩ EB ∩ CF at M

∴ M is the point of intersection of the medians of Δ AEC

→ By using the rule above

∴ AD = 3 MD

∵ MD = 5

∴ AD = 3(5)

∴ AD = 15 units

statuscvo [17]3 years ago

6 0

Answer:

the answer is 15!! i jus took the test!!!!!!

Step-by-step explanation:

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lapo4ka [179]

Answer:

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Step-by-step explanation:

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3 years ago

FLAGPOLE Julie is 6 feet tall. If she stands 15 feet from the flagpole and holds a cardboard square, the edges of the square lin

Soloha48 [4]

Answer:

44 ft

Step-by-step explanation:

Given: Julie is 6 feet tall

She stands 15 feet from the flagpole.

The edges of the square line up with the top and bottom of the flagpole.

Lets assume the height of flagpole be "h".

As given, the edges of the square line up with the top and bottom of the flagpole.

∴ Angle and base of triangle are same then ratio of corresponding sides are also equal.

Now, finding the height of flagpole by using tangent rule.

we know, $tan\theta= \frac{Opposite}{adjacent}$

Remember, both the angle are equal.

∴ Ratio of opposite and adjacent leg for both right angle triangle= $\frac{6}{15} : \frac{h-6}{15}$

We can put it; $\frac{6}{15} = \frac{15}{h-6}$

Solving the equation now

⇒ $\frac{6}{15} = \frac{15}{h-6}$

Multiplying both side by 15

⇒ $6 = \frac{15\times 15}{h-6}$

Multiplying both side by (h-6)

⇒ $6\times (h-6) = 15\times 15$

Distributive property of multiplication

⇒ $6h-36= 225$

Adding both side by 36

⇒ $6h= 225+36$

Dividing both side by 6

⇒ $h= \frac{261}{6}$

∴ $h= 43.5\ feet$ $\approx 44 feet$

Hence, the height of flagpole is 44 feet.

8 0

3 years ago