The lengths of the sides of $△ A B C$ are $3$ cm, $4$ cm, and $6$ cm. Determine the least possible perimeter of a triangle similar to $△ A B C$ which has one side of length $12$ cm?

Open in App

Solution

Similar triangles have the same shape because they have the same angles.
They are of different sizes, but their sides are in the same ratio.
In $△ A B C,$ the sides are $3 : 4 : 6$
For the smallest perimeter of the other triangle, the longest side must be
$12$ cm. The sides will $∴$ all be twice as long.
$△ A B C : 3 : 4 : 6$
New $△ : 6 : 8 : 12$
The perimeter of $△ A B C = 6 + 4 + 3 = 13$ cm
The perimeter of the second triangle will be $13 \times 2 = 26$ cm

Suggest Corrections

Similar questions

Q. The sides of

Δ ABC

are 6 cm, 8 cm and 10 cm. Find the perimeter of the larger triangle which is similar to

Δ ABC

if the ratio of corresponding sides is 2.

The sides of $Δ ABC$ are $6 c m, 8 c m$ and $10 c m .$ Find the perimeter of the larger triangle which is similar to $Δ ABC$ if the ratio of corresponding sides is 2.

Q. The sides of

Δ ABC

have sides AB, BC, AC as

2 c m, 4 c m, and 6 c m

respectively. Find the sides of the larger triangle which is similar to

Δ ABC

, if the ratio of corresponding sides is

3

The sides of $Δ ABC$ are $6 c m, 8 c m$ and $10 c m .$ Find the sides of the larger triangle which is similar to $Δ ABC$ if the ratio of corresponding sides is 2.

$△ A B C$ , right angled at B, BC = 6 cm and ∠ABC = $30^{\circ}$ . Determine the length of the side AB and AC.

Join BYJU'S Learning Program

The lengths of the sides of △ABC are 3 cm, 4cm, and 6 cm. Determine the least possible perimeter of a triangle similar to △ABC which has one side of length 12 cm?

The lengths of the sides of $△ A B C$ are $3$ cm, $4$ cm, and $6$ cm. Determine the least possible perimeter of a triangle similar to $△ A B C$ which has one side of length $12$ cm?