Question

2
13. Each of the two equal sides of a triangle are 4 m less than three times the third side
Find the dimensions of the triangle, if its perimeter is 55 m​

Answer 1

Given

• Each of the two equal sides of a triangle are 4 m less than three times the third side.
• Perimeter of the triangle = 55 m

To find

• Dimensions of the triangle

Concept

We are given that the triangle has two equal sides which are 4 m less than three times the third side. So, it is an Isosceles triangle.

Firstly, we will let the third side as x and the other two equal sides as 3x - 4. We have the value of the perimeter of the triangle, by using the formula of perimeter of triangle we will find the value of x. By substituting the value of x in the sides which we have let, we will find the dimensions of the triangle.

Answer

$\bigstar$ Dimensions of the triangle :-

$\mapsto$Two equal sides = 23 m

$\mapsto$ Third side = 9 m

Solution

Let the third side of the triangle be x m and the two equal sides be (3x - 4) m

$\dag\boxed{ \bf \purple{perimeter \: of \: the \: equilateral \: triangle = 2a + b}} \pink\bigstar$

where,

• a = two equal sides
• b = third side

Substituting the values,

$\quad : \implies \sf \gray{55 = 2(3x - 4) + x} \\ \\ \\ \quad : \implies \sf \gray{55 = 6x - 8 + x} \\ \\ \\ \quad : \implies \sf \gray{55 = 7x - 8} \\ \\ \\\quad : \implies \sf \gray{55 + 8 = 7x} \\ \\ \\ \quad : \implies \sf \gray{63 = 7x} \\ \\ \\ \quad : \implies \sf \gray{ \dfrac{63}{7} = x} \\ \\ \\ \quad : \implies \sf \gray{ \dfrac{ \cancel{63}}{ \not7} = x } \\ \\ \\ \quad : \implies \sf \gray{9 = x} \\ \\ \\ \quad \therefore \tt \pink{the \: value \: of \: x = 9} \bigstar$

Substituting the value of x in the sides of the triangle.

• The two equal sides = 3x - 4 = 3 × 9 - 4 = 27 - 4 = 23 m
• The third side = x = 9 m

________________________________________

$\underbrace{ \bf \pink {let's \: verify} : } \\ \\ \\ \quad : \implies \sf \gray{55 = 2(3x - 4) + x} \\ \\ \\ \quad \sf \red{ \large{ \underline{Rhs}}} \\ \\ \\ \quad : \diamond \: \sf {substituting \: the \: value \: of \: x \: in \: 2(3x - 4) + x} \\ \\ \\ \quad : \implies \sf \gray{2(3 \times 9- 4) + 9} \\ \\ \\ \quad : \implies \sf \gray{2(27 - 4) + 9} \\ \\ \\ \quad : \implies \sf \gray{2(23) + 9} \\ \\ \\ \quad : \implies \sf \gray{46 + 9} \\ \\ \\ \quad : \implies \sf \orange{55} \\ \\ \\ \quad \bf {Lhs = Rhs} \\ \\ \\ \quad \bf \dag \: \red{hence \: verified}$

Answer 2

❒Given:

↝Each of the two equal sides of a triangle are 4 m less than three times the third side.

↝Perimeter of the triangle = 55 m

❒To find:

↝Dimensions of the triangle

❒Solution:

↝Let the third side of the triangle be x m and the two equal sides be (3x - 4) m

$\mathcal\pink{Perimeter \:of \: equilateral\: triangle: \: \: 2a+b}$

where,

• a = two equal sides
• b = third side

Substituting the values,

↬55=2(3x−4)+x

↬55=6x−8+x

↬55=7x−8

↬55+8=7x

↬63=7x

↬$\frac{63}{7} = x$

↬$9 = x$

∴thevalueofx=9

Substituting the value of x in the sides of the triangle.

The two equal sides

=>3x - 4

=>3 × 9 - 4

=>27 - 4

=>23m

$\mathcal\purple{Verification}$

↳55=2(3x−4)+x

RIGHT HAND SIDE:

substituting thebvalue of x in 2(3x−4)+x

⇝2(3×9−4)+9

⇝2(27−4)+9

⇝2(23)+9

⇝46+9

⇝55

LHS=RHS

†hence verified

______________________________

$\mathcal\purple{Final\: Answer}$

$\mathcal\pink{2\:equal\:sides\: =23m}$

$\mathcal\purple{2rd\:side\:= 9m}$

$\huge\mathbb{\pink{ハンはジャクソンが大好き}}$