Question

the longest side of a triangle is twice the shortest side and the third side is 2 cm longer than the shorter side if the perimeter of the triangle is more than 166 cm
then find the minimum length of the shorter side​

Answer 1

Let longest and shortest sides of triangle are x and y respectively.

a/c to question,

x = 2y ......(1)

third side (let z) = 2 + y .....(2)

now, perimeter of triangle = sum of sides of triangle

⇒166 ≤ x + y + z

from equations (1) and (2),

⇒166 ≤ 2y + y + y + 2

⇒166 ≤ 4y + 2

⇒164 ≤ 4y

⇒y ≥ 41

so, minimum value of y = 41

hence, minimum length shorter side is 41cm.

Answer 2

Answer:

Let longest and shortest sides of triangle are x and y respectively.

a/c to question,

x = 2y ......(1)

third side (let z) = 2 + y .....(2)

now, perimeter of triangle = sum of sides of triangle

⇒166 ≤ x + y + z

from equations (1) and (2),

⇒166 ≤ 2y + y + y + 2

⇒166 ≤ 4y + 2

⇒164 ≤ 4y

⇒y ≥ 41

so, minimum value of y = 41

hence, minimum length shorter side is 41cm.