I need Help! please I don't understand

AM is a median in △ABC (M∈ BC ). A line drawn through point M intersects AB at its midpoint P. Find areas of △APC and △PMC, if A

Snowcat [4.5K]

Answer:

The area of APC is 70m². The area of triangle PMC is 35m².

Step-by-step explanation:

Let the area of triangle ABC be x.

It is given that AM is median, it means AM divides the area of triangle in two equal parts.

$\text{Area of }\triangle ACM=\text{Area of }\triangle ABM=\frac{x}{2}$ .....(1)

The point P is the midpoint of AB, therefore the area of APC and BPC are equal.

$\text{Area of }\triangle APC=\text{Area of }\triangle BPC=\frac{x}{2}$ ......(2)

The point P is midpoint of AB therefore the line PM divide the area of triangle ABM in two equal parts. The area of triangle APM and BPM are equal.

$\text{Area of }\triangle APM=\text{Area of }\triangle BPM=\frac{x}{4}$ .....(3)

The area of triangle APM is 35m².

$\text{Area of }\triangle APM=\frac{x}{4}$

$35=\frac{x}{4}$

$x=140$

Therefore the area of triangle ABC is 140m².

Using equation (2).

$\text{Area of }\triangle APC=\frac{x}{2}$

$\text{Area of }\triangle APC=\frac{140}{2}$

$\text{Area of }\triangle APC=70$

Therefore the area of triangle APC is 70m².

Using equation (3), we can say that the area of triangle BPM is 35m² and by using equation (2), we can say that the area of triangle BPC is 70m².

$\triangle BPC=\triangle BPM+\triangle PMC$

$70=35+\triangle PMC$

$35=\triangle PMC$

Therefore the area of triangle PMC is 35m².

8 0

3 years ago

Please solve with working thankyou

Lisa [10]

Answer:

m∠y=72°

Step-by-step explanation:

<u><em>The question is</em></u>

Find the measure of angle y

step 1

Find the measure of angle x

see the attached figure to better understand the problem

we know that

m∠x=67° -----> by corresponding angles

step 2

Find the measure of angle y

we know that

(m∠x+m∠y)+42°=180° -----> because form a straight line

substitute the measure of angle x

67°+m∠y+42°=180

m∠y+108°=180

m∠y=180°-108°

m∠y=72°

4 0

2 years ago

Which expression is equivalent to −6(23−12)?

Softa [21]

Answer:

C

Step-by-step explanation:

5 0

2 years ago

Consider the function represented by the equation y-6x-9=0. Which answer shows the equation written in function notation with x

hichkok12 [17]

Y=6X+9 the A is #1
all you need to do is simp the equation

4 0

3 years ago

Read 2 more answers

The distance on the map between Yappy City and Quiet City is 23 cm. What is the actual distance between the cities? 5 cm : 2 mil

S_A_V [24]

The actual distance between the cities will be equal to 9.2 miles.

<h3>What is an arithmetic operation?</h3>

The four basic mathematical operations are the addition, subtraction, multiplication, and division of two or even more integers. Among them is the examination of integers, particularly the order of actions, which is crucial for all other mathematical topics, including algebra, data organization, and geometry.

As per the given data in the question,

Distance between Yappy city and quit city is 23 cm.

As per the conversion is given in the question,

5 cm = 2 miles

Then, the number of miles of distance will be,

x = (2 × 23)/5

x = 9.2 miles.

To know more about arithmetic operations:

brainly.com/question/13585407

#SPJ1

3 0

1 year ago

I need Help! please I don't understand​

I need Help! please I don't understand