The perimeter of a triangle

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

2 years ago

A television weighs 50 pounds and a microwave

Ilia_Sergeevich [38]

Answer:

Step-50*t + 30*m = 1500, (1) (pounds)

4*t + 3*m = 138. (2) (cubic feet)

From (2), express 3m = 138 - 4t, and substitute it into (1). You will get

50t + 10*(138-4t) = 1500, or

10t = 1500 - 1380 ---> 10t = 1120 ---> t = 112 TVs.

From this point, find the number of microwaves on your own.

step by-step explanation:

3 0

2 years ago

How do you do -19+C/3=8 can someone teach how to solve this problem?

ki77a [65]

You're looking for c, so you want to isolate it or get it by itself. To get rid of the /3 you multiply since the opposite of division is multiplication and to get rid of it, you do the opposite (like -9 you would add 9 to get it to 0). Now you are left with -19+c = 24 (the 24 is 8*3 because what you do to one side you do to the other. Now you get c by itself so you add 19 to both sides which leaves you with C= 43. Sorry if this was confusing!

3 0

3 years ago

There are 870 boys and 800 girls in a school

alina1380 [7]

Answer:

1060

Step-by-step explanation:

Given:

No. of boys = 870

No. of girls = 800

Probability that a boy chosen studies Spanish = $\dfrac{2}{3}$