Please help me I don’t get this and it’s due soon

The three sides of a triangle are (x+5)cm ,(2x+4)cm and (2x-3)cm .

natali 33 [55]

Hey ! there

Answer:

a. Perimeter = ( 5x + 6 ) cm

b. Perimeter when x is equal to 10 = 56 cm

Step-by-step explanation:

In this question we are given with three sides of a triangle that are as follows ,

 ( x + 5 ) cm

 ( 2x + 4 ) cm

 ( 2x - 3 ) cm

And we are asked to :

a. find perimeter of triangle.

b. find perimeter if x is equal to 10 .

We know that for finding perimeter of any shape we must have to add all the sides of the shape or ,

$\qquad \: \underline{\boxed{\frak{Perimeter = Sum \: of \: all \: sides}}}$

Solution : -

( a )

Now adding all the three sides of triangle to find the perimeter .

$\hookrightarrow \quad \: ( x + 5 ) + ( 2 x + 4 ) + ( 2x - 3 )$

$\hookrightarrow \quad \: \: x + 5 + 2x + 4 + 2x - 3$

Combining like terms :

$\hookrightarrow \quad \:x + 2x + 2x + 5 + 4 - 3$

Now , solving :

$\hookrightarrow \quad \: \red{\underline{ \boxed{ \frak{(5x + 6) \: cm}}}}$

Therefore , perimeter of triangle is 5x + 6 centimetres .

( b )

Now , we are finding perimeter of triangle when value of x is 10 . So substituting value of x in given sides of triangle ,

First Side :

x + 5

10 + 5

15 cm

Second Side :

2x + 4

2 ( 10 ) + 4

20 + 4

24 cm

Third Side :

2x - 3

2 ( 10 ) - 3

20 - 3

17

So , all the sides are 15 cm , 24 cm and 17 cm .

Now , adding all these to find perimeter . 

 $\hookrightarrow \qquad \: 15 + 24 + 17$ 

 $\hookrightarrow \qquad \: 39 + 17$ 

 $\hookrightarrow \qquad \: \red{\underline{\boxed{\frak{56 \: cm}}}}$ 

Therefore , perimeter of triangle when value of x is 10 cm is 56 cm .

Alternative Solution : -

As above we have find the perimeter of triangle in term of x that is ( 5x + 6 ) cm. So we can put value of x as 10 in this to get perimeter. So ,

5x + 6

5 ( 10 ) + 6

50 + 6

56 cm

Therefore, perimeter of triangle is 56 cm .

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