s0cial0bessi0n

14.01.2021 •

Mathematics

A little help please.
if you cant see just click on the photo...

A little help please.if you cant see just click on the photo...

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Ответ:

keymariahgrace85

21.12.2021

Mathematics

Answer : The area of ΔABC is, $1787.06\text{ inches}^2$

Step-by-step explanation :

Given:

Side AM = 48 inches

Side AC = 40 inches

Side BC = 100 inches

First we have to determine the side CM and side BM.

As, AM is a median of an acute triangle ABC. So, median divides the side BC into two equal side.

That means,

Side CM = Side BM = $\frac{100}{2}$ = 50 inches

Now we have to determine the semi-perimeter of ΔAMC.

Formula used :

$s=\frac{AM+MC+AC}{2}$

$s=\frac{48+50+40}{2}$

s=69

Now we have to determine the area of ΔAMC.

Using Heron's formula:

$A=\sqrt{s(s-a)(s-b)(s-c)$

where,

A is a area, s is a semi-perimeter and a, b, c are the sides of triangle.

$A=\sqrt{69(69-48)(69-50)(69-40)$

$A=893.53\text{ inches}^2$

Thus, the area of ΔAMC = $893.53\text{ inches}^2$

Now we have to determine the area of ΔABC.

As we know that, each median of a triangle divides the triangle into two smaller triangles which have equal area.

So,

ΔABC = 2 × ΔAMC

ΔABC = $2\times 893.53\text{ inches}^2$

ΔABC = $1787.06\text{ inches}^2$

Thus, the area of ΔABC is, $1787.06\text{ inches}^2$

Am is a median of an acute triangle abc. the distance of the point m from the side ab is 48 inches,

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