Question

an equilateral triangle has sides of length x+1 cm
an square has the sides of x-2 cm
The triangle and the square have the same perimeter

A) write down an equation in terms of x that links the perimeter of each shape
b) Solve the equation to find value of x
c) Write down the length of each side of the square

2

Answer 1

Given,

An equilateral triangle has sides of length (x+1)cm  and a square has the sides of (x-2)cm  . The triangle and the square have the same perimeter

To find :

A) Write down an equation in terms of x that links the perimeter of each shape .

b) Solve the equation to find value of x.

c) Write down the length of each side of the square .

Solution :

Side of equilateral triangle = (x + 1) cm

Side of square = (x - 2) cm

Perimeter of equilateral triangle = Perimeter of square

Now we know,

→ Perimeter of equilateral triangle = 3 * Side

→ Perimeter of square = 4 * Side

Now atq,

⇒ 3(x + 1) = 4(x - 2)           [Answer of (A)]

Now solving the equation :

⇒ 3x + 3 = 4x - 8

⇒ 4x - 3x = 8 + 3

⇒ x = 11                [Answer of (b)]

Now length of each side of square :

⇒ Side of square = x - 2

⇒ Side of square = 11 - 2

⇒ Side of square = 9 cm           [Answer of (c)]

Answer 2

$\huge{\boxed{\rm{Question}}}$

An equilateral triangle has sides of length x+1 cm. A square has the sides of x-2 cm.

The triangle and the square have the same perimeter.

• Write down an equation in terms of x that links the perimeter of each shape.

• Solve the equation to find value of x.

• Write down the length of each side of the square.

$\huge{\boxed{\rm{Answer}}}$

$\large{\boxed{\boxed{\sf{Given \: that}}}}$

• An equilateral triangle has sides of length x+1 cm.

• A square has the sides of x-2 cm.

• The triangle and the square have the same perimeter.

$\large{\boxed{\boxed{\sf{To \: find}}}}$

• Write down an equation in terms of x that links the perimeter of each shape.
• Solve the equation to find value of x = 11.

• Write down the length of each side of the square.

$\large{\boxed{\boxed{\sf{Solution}}}}$

• Write down an equation in terms of x that links the perimeter of each shape = 3(x+1) = 4(x-2)

• Solve the equation to find value of x = 4(x-2)

• Write down the length of each side of the square = 9

$\large{\boxed{\boxed{\sf{Using \: formulas}}}}$

• Perimeter of equaliteral triangle = 3 × Side.

• Perimeter of square = 4 × Side.

$\large{\boxed{\boxed{\sf{We \: also \: write \: these \: as}}}}$

• Perimeter as P.

• Triangle as ∆.

• Length as L.

$\large{\boxed{\boxed{\sf{What \: does \: the \: question \: says}}}}$

$\large{\boxed{\boxed{\sf{Let's \: understand \: the \: concept \: 1st}}}}$

• This question says that an equilateral triangle has sides of length x+1 cm. A square has the sides of x-2 cm. The triangle and the square have the same perimeter. In this We have to find the following data

➜ Write down an equation in terms of x that links the perimeter of each shape. In this part we have to write the equation by using given formulas.

➜ Solve the equation to find value of x. In this part using the equation we have to find the value of x.

➜ Write down the length of each side of the square. In this part we have to solve this by substituting the value of x form above answer.

$\large{\boxed{\boxed{\sf{How \: to \: solve \: this \: question}}}}$

$\large{\boxed{\boxed{\sf{Let's \: see \: the \: procedure \: now}}}}$

• To solve this question we have to know some formulas that are mentioned above by me. So plzz see them to understand the concept properly. Now solving question 1 putting the values according to the formula. We get our result. Now solving question 2. Using above answer ( question 1 ) we have to find the value of x. After putting the values we get our result property. Solving question 3. By substituting the value of x that is the result of question 2. And we get our result very easily. See below to know the procedure properly.

$\large{\boxed{\boxed{\sf{Full \: solution}}}}$

According to the question it is cleared that what is given or what to find ! Let's see it again properly !!

• An equilateral triangle has sides of length x+1 cm. ( Given )
• A square has the sides of x-2 cm. ( Given )

• The triangle and the square have the same perimeter. ( Given )

• Write down an equation in terms of x that links the perimeter of each shape. ( To find )
• Solve the equation to find value of x. ( To find )

• Write down the length of each side of the square. ( To find )

Answer 1.

According to the question, let's carry on the equation is given below

• 3(x+1) = 4(x-2)

Answer 2.

According to the question, let's carry on

• 3(x+1) = 4(x-2)
• 3x + 3 = 4x - 8
• 3x - 4x = -8 -3
• -1x = -11
• 1x = 11
• x = 11/1
• x = 11.

Answer 3.

According to the question, let's carry on

L of each side of square

• Side of square = x - 2

Substituting the value of x that is 11.

• Side of square = 11 - 2
• Side of square = 9.