Question

3) In A ABC, M and N are the mid points of AB: and AC respectively. If AB = 8cm, AC = 7 cm,
MN = 4.5 cm, find the perimeters of A ABC​

Answer 1

Given:

• AB = 8cm
• AC = 7cm
• MN = 4.5cm

Find:

• Perimeter of $\triangle$ ABC

Diagram:

$\setlength{\unitlength}{1cm} \begin{picture}(6,6) \thicklines \put(2,2){\line(1,1){2}}\put(4,4){\line(1,-1){2}} \put(2,2){\line(1,0){4}} \put(2,1.6){\sf B}\put(4,4.1){\sf A}\put(5.9,1.6){\sf C} \put(2.5,3){\vector(1,1){1}}\put(2.5,3){\vector( - 1, - 1){0.6}}\put(1.8,3){\sf 8cm} \put(5.6,3){\vector( - 1,1){1}}\put(5.8,3){\sf 7cm} \put(5.6,3){\vector(1, - 1){0.6}}\put(3,3){\line(1,0){2}} \put(2.7,3){\sf M} \put(5.1,3){\sf N} \put(3.8,2.6){\sf 4.5cm} \put(3.1,4.6){\sf made by @BLACKSKULL}\end{picture}$

Solution:

Here, M is mid-point AB and N is mid-Point of AC

So,

$\sf MN \parallel BC$

$\sf and,MN = \dfrac{1}{2} BC$

Since, Mid-point Theorem

$\sf so, BC = 2MN$

where,

• MN = 4.5cm

So,

$\sf :\to BC = 2MN$

$\sf :\to BC = 2(4.5)$

$\sf :\to BC = 8cm$

$\sf \therefore BC = 8cm$

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we, know that

$\boxed{ \sf Perimeter \: of \: triangle,s = a + b + c }$

where,

• AB, a = 8cm
• AC, b = 7cm
• BC, c = 8cm

So,

$\dashrightarrow\sf Perimeter \: of \: triangle,s = a + b + c$

$\dashrightarrow\sf Perimeter \: of \: triangle,s = 8 + 7 + 8$

$\dashrightarrow\sf Perimeter \: of \: triangle,s = 23cm$

$\dashrightarrow\sf s = 23cm$

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Hence, Perimeter of given ∆ ABC is 23cm