Question

11. If two equal sides of an isosceles triangle are (4x - 2) cm and (3x + 1) cm and the third side is
(2x - 1) cm, then its perimeter is
a. 35 cm.
b. 20 cm.
c. 15 cm.
d. 25 cm​

Answer 1

It is given that the two equal sides are (4x-2) and (3x+1)

So, 4x - 2 = 3x + 1

=> x = 3

Thus, the sides are-

4x - 2 = 4×3 - 2 = 12-2 =10cm

3x +1 = 3×3 + 1 = 9 + 1 = 10 cm

2x - 1 = 2×3 - 1 = 6 - 1 = 5 cm

Therefore, Perimeter = 10 + 10 + 5 = 35 cm.

Answer 2

GivEn:-

✠ Sides of isosceles triangle are:-

⠀⠀⠀✩⠀(4x - 2) cm

⠀⠀⠀✩⠀(3x + 1) cm

⠀⠀⠀✩⠀(2x - 1) cm

where,

• (4x - 2) cm and (3x + 1) cm are the equal sides of that triangle.

To find:-

• Perimeter of isosceles triangle.

SoluTion:-

☯ It is an Isosceles triangle where (4x - 2) cm and (3x + 1) cm are the equal sides.

$\small\sf\;\;\;\;\dag\; \underline{Now,\;equate\;it:-}$

$:\implies\sf (4x - 2) = (3x + 1)$

$:\implies\sf 4x - 3x = 1 + 2$

$:\implies{\underline{\boxed{\bf{\pink{x = 3}}}}}$ ★

☯ Now, substitute value of x in all measures of triangle

✠ Sides of triangle,

• (4x - 2) = (4 × 3 - 2) = 12 - 2 = 10cm

• (3x + 1) = (3 × 3 + 1) = 9 + 1 = 10cm

• (2x - 1) = (2 × 3 - 1) = 6 - 1 = 5cm

Now,

☯ For finding Perimeter of the triangle we have to add all sides of triangle,

$\star\;\sf Perimeter = (4x - 2) + (3x + 1) + (2x - 1)$

$:\implies\sf 10cm + 10cm + 5cm$

$:\implies\sf 20cm + 5cm$

$:\implies{\underline{\boxed{\bf{\blue{25\;cm}}}}}$ ★

$\dag$ Perimeter of givEn isosceles triangle is 25cm.

$\therefore$ OpTion (D) is correct AnswEr.

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