Question

the perimeter of triangle is 49 cm and one side is 7cm more than the second side and 5cm less than third side find the lenght of each three sides
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Answer 1

Answer:

Let's assume one side be xso, one side= x-7and another side= x+5so, x+(x-7)+(x+5)=493x-2=493x=49+23x=51x=51/3x=17so, the sides are17,(17-7),(17+5)17,10,22Hence, the numbers are 17,10 and 22 respectively.

Answer 2

Question :-

the perimeter of triangle is 49 cm and one side is 7cm more than the second side and 5cm less than third side find the length of each three sides.

Answer :-

• First side = 10
• Second side = 22
• Third side = 17

Step by step explanation :-

Let first understand the question in detail.

The question is a perimeter of a triangle is 49cm. First side is more 7cm than the 2nd side and the second side is 5cm less than third side. Here, we have to find the actual measure of the sides. Now, we have to the measure of sides for that we have first assume the all sides by taking a variable.

On understanding the question,

We take the x variable to assume the all sides of that triangle.

Assumption :-

• First side = x - 7
• Second side = x + 5
• Third side = x

We know that,

$\rm:\longmapsto{Perimeter_{(\triangle)} = a + b + c }$

Here, a, b and c are the sides of triangle.

On substituting all values we get,

$\rm:\longmapsto{49 = (x - 7) + (x + 5) + x}$

On opening brackets,

$\rm:\longmapsto{49 = x - 7 + x + 5 + x}$

Adding all x and taking a side,

$\rm:\longmapsto{49 = 3x - 2}$

Transporting -2 to LHS because of that -2 convert into +2 .

$\rm:\longmapsto{3 x = 51}$

Transporting 3 to RHS in LHS 3 is in multiply after transporting convert into divide 3.

$\rm:\longmapsto{x = \frac{51}{3} }$

$\bf:\longmapsto \red{x = 17}$

Now, we got the value of x now substitute the value of x in the measure of sides of triangle then we get actual measures of sides of triangle.

First Side :

⇒ x - 7

⇒ 17 - 7

⇒ 10

Second side :

⇒ x + 5

⇒ 17 + 5

⇒ 22

Third side :

⇒ x

⇒ 17

Additional Information :-

Formula of perimeter of triangle :-

$\rm:\longmapsto{Perimeter_{(\triangle ) } = a + b + c}$

Formula of area of triangle by heron's formula :-

$\rm:\longmapsto{Area_{(\triangle ) } = \sqrt{s(s - a)(s - b)(s - c)} }$

Formula of semi perimeter :-

$\rm:\longmapsto{Semi \: perimeter_{(\triangle ) } = \frac{a + b + c}{2} }$

Formula of Area of triangle by using base and height :-

$\rm:\longmapsto{Area_{(\triangle ) } = \frac{1}{2} \times base \times height }$

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