Question

$\huge\fbox\red{h}\fbox\green{e}\fbox\blue{l}\fbox\orange{l}\fbox\purple{o}$
⚝Solve the following equation and verify-
➠15(x - 4) - 2(x + 3) - 3(x + 8) =0

⚝In a triangle, the longest side is double the shortest side and the third side is 3 cm less than the longest side. If the perimeter is 27 cm, find all tge sides of the triangle.
__________________
✯Kindly Answer both questions!
✯No Spam!
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Answer 1

★ Answer ★

15(x - 4) - 2(x + 3) - 3(x + 8) =0

➠ 15x - 60 - 2x - 6 -3x + 24

➠ 10x - 66 - 24

➠ 10x -90

➠ x = 10/90

➠ x = 9

__________________

•Let Longest side = x.

•hortest side = x/2

•Third side = x -3

Perimeter = x + x/2 +x -2

= 5x/2 -x

Given

➠5x/2- 3 = 27

➠5x/2 = 30

➠x = 12

Sides are :-

12 , -12/2 , 12-3

So,

12cm, -6cm, 9cm

Answer 2

Let's solve both the questions one by one!

$\underline{\boxed{ \bf Answer \: 1:-}}$

The value of x = 9.

Step-by-step explanation :-

$\sf Q) \: 15 \: (x - 4) - 2 \: (x + 3) - 3 \: (x + 8) = 0$

• Removing the brackets by simplifying,

$\sf\Rightarrow15x - 60 - 2x - 6 - 3x - 24 = 0$

• Putting the constants and the variables on separate sides by transposing,

$\sf\Rightarrow15x - 2x - 3x = 0 + 60 + 6 + 24$

• On simplifying,

$\sf\Rightarrow15x - 5x = 66 + 24$

• On simplifying the numbers again,

$\sf\Rightarrow10x = 90$

• Transposing 10 from LHS to RHS, changing it's sign,

$\sf \Rightarrow x = \dfrac{90}{10}$

• Dividing 90 by 10,

$\underline{ \boxed{ \sf \Rightarrow x = 9.}}$

• The value of x = 9.

Verification :-

To check our answer, let's put 9 in place of x and see whether LHS = RHS.

Substituting the values,

LHS

$\sf\Rightarrow15 \: (9 - 4) - 2 \: (9 + 3) - 3 \: (9 + 8)$

• Simplifying the numbers inside the brackets,

$\sf\Rightarrow15 \: (5) - 2 \: (12) - 3 \: (17)$

• Removing the brackets,

$\sf\Rightarrow15 \times 5 - 2 \times 12 - 3 \times 17$

• On simplifying,

$\sf\Rightarrow75 - 24 - 51$

• Subtracting the numbers,

$\sf\Rightarrow0.$

RHS

$\Rightarrow \sf0.$

Since LHS = RHS,

Hence verified!

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$\underline{\boxed{ \bf Answer \: 2:-}}$

• The sides of the triangle are 6 cm, 12 cm and 9 cm.

Given :-

• The longest side is double of the shortest side.

• The third side is 3 cm less than the longest side.

• The perimeter is 27 cm.

To find :-

• All the sides of the triangle.

Step-by-step explanation :-

Let the shortest side of the triangle be x.

The longest side is double of the shortest side, therefore it will be 2x.

• Now, the third side is 3 cm less than the longest side, which means that it's 3 cm less than 2x. Hence it's value will be 2x - 3.

We know that :-

$\underline{ \fbox{ \sf Perimeter of a triangle = Sum of all sides.}}$

• So, these three sides must be equal to 27 cm, since it's the perimeter of the triangle.

$\sf \implies x + 2x + 2x - 3 = 27$

• Adding x, 2x and 2x,

$\sf \implies5x - 3 = 27$

• Transposing 3 from LHS to RHS, changing it's sign,

$\implies\sf5x = 27 + 3$

• Adding the numbers,

$\implies \sf5x = 30$

• Transposing 5 from LHS to RHS, changing it's sign,

$\implies\sf x = \dfrac{30}{5}$

• Dividing 30 by 5,

$\underline{ \boxed{ \implies\sf x = 6. }}$

• The value of x = 6.

Hence, all the sides are as follows :-

$\implies \tt x = 6.$

$\implies \tt2x = 6 \times 2 = 12.$

$\implies \tt2x - 3 = 2 \times 6 - 3 = 12 - 3 = 9.$