Question

A triangle has a perimeter of 165cm the first side is 65 cm less than twice the second side the third side is 10 cm less than the second side find the length of each side of the triangle what equation represents the perimeter of the triangle if the second side is length s

Answer 1

Answer:

The sides of the triangle are:

Second side = 60 cm

First side = 55 cm

Third side = 50 cm

The perimeter equation can be given as:

$4s-75=165$

Step-by-step explanation:

Given:

Perimeter of triangle = 165 cm

First side = 65 cm less than twice the second side

Third side = 10 cm less than the second side

To find length of each side and write the equation that represents the perimeter of triangle.

Solution:

Let length of second side be = $s$ cm

First side will be given as = $(2s-65)$ cm

Third side will be given as =  $(s-10)$ cm

Perimeter of triangle = Sum of all sides

Thus, perimeter can be given as:

⇒ $First\ side+ Second\ side+Third\ side$

⇒ $2s-65+s+s-10$

Simplifying by combining like terms.

⇒ $4s-75$

We know the perimeter of triangle = 165 cm

So, the perimeter equation can be given as:

$4s-75=165$

Solving for $s$.

Adding 75 both sides.

$4s-75+75=165+75$

$4s=240$

Dividing both sides by 4.

$\frac{4s}{4}=\frac{240}{4}$

$s=60$

Thus, the sides of the triangle are:

Second side = 60 cm

First side = $2(60)-65$ = 55 cm

Third side = $60-10$ = 50 cm

Answer 2

FIRST, we need variables. Once we define variables, it's much easier to turn this word problem into a math problem.

Let a = first side

Let b = second side

Let c = third side

NOW, we can turn the words into equations:

"a triangle has a perimeter of 165 cm."

a + b + c = 165

"the first side is 65cm less than twice the second side."

a = 2b - 65

"the third side is 10cm less than the second side."

c = b - 10

Before we finish, I have to ask: Who writes problems like this??? Pointless problems like these are why kids don't like math! Ugh. Drives me crazy. It's a shame, because solving math problems really does have a certain satisfaction, once you learn how. [Okay. I'm done. Back to the problem.]

If we could get this to have only one variable, we could solve it. Substitution to the rescue!

 

a + b + c = 165 (rewrote equation from above)

(2b - 65) + b + (b - 10) = 165 (substituted "a" and "c" from equations above)

See how that works? Let's solve it.

2b - 65 + b + b - 10 = 165 (dropped the parentheses, because there was nothing to distribute, not even a minus sign)

4b - 75 = 165 (combined like terms)

4b = 240 (added 75 to both sides)

b = 60 (divided both sides by 4)

We found the second side! We can find the first and third sides using those equations from above:

a = 2b - 65

a = 2*60 - 65

a = 120 - 65

a = 55

c = b - 10

c = 60 - 10

c = 50

All done.

PLEASE MARK ME AS BRAINLIEST