Question

If the two sides of an equilateral triangle measure
1/4(3x+1) units and 1/3(4x-1)units then what is theperimeter of the triangle?
(1)3 sq, units
(2) 3 units
(3)-3 units
(4) 1/3 units ​

Answer 1

Answer:

The perimeter is 3 units and side length is 1 units.

Step-by-step explanation:

Equate given side lengths and find x for solution.

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Answer 2

Given :-

• one side of an equilateral triangle = 1/4(3x + 1) units
• other side of an equilateral triangle = 1/3(4x -1) units

To Find :-

• perimeter of the triangle ?

Solution :-

we know that,

all sides of equilateral triangle are equal to each other

$\bold{: \implies \frac{1}{4}(3x + 1) = \frac{1}{3} (4x - 1) } \\ \\ \bold{: \implies \frac{3x + 1}{4} = \frac{4x - 1}{3} } \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \bold{: \implies 3(3x + 1) = 4(4x - 1)} \: \: \\ \\ \bold{: \implies 9x + 3 = 16x - 4} \: \: \: \: \: \: \: \: \: \: \: \\ \\ \bold{: \implies 9x - 16x = - 4 - 3 } \: \: \: \: \: \: \: \: \\ \\ \bold{: \implies - 7x = - 7 } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \bold{: \implies x = \cancel\frac{ - 7}{ - 7} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \bold{ : \implies x = 1 } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

then, sides of the equilateral triangle are

$\frac{1}{4} (3 \times 1 + 1) \\ \\ \bold{\implies \frac{3 + 1}{4} } \: \: \: \: \\ \\ \bold{ \implies \cancel\frac{4 }{4} } \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \bold{ \implies 1} \: \: \: \: \: \: \: \: \: \: \: \: \:$

so, Length of all sides of the equilateral triangle is 1 units

now, we know that;

$\boxed{ \bold{perimeter \: of \: equi. \triangle = 3 \times sides}}$

$\bold{: \implies 3 \times 1} \: \: \: \: \\ \\ \bold{: \implies 3 \: units}$

hence, perimeter of the triangle is 3 units

option (2) is correct