Question

Areas of two similar triangles are 36 sq. cm and 16 sq. cm. If a side of the smaller triangle is 12 cm, then find corresponding side of the bigger triangle. *​

Answer 1

Answer:

• Corresponding side of bigger triangle would be 27 cm

Explanation:

Given,

• Area of two similar triangle are 36 cm² and 16 cm²
• Side of smaller triangle is 12 cm

To find,

• Corresponding side of bigger triangle, x =?

Knowledge required,

• Theorem for Area of similar triangles

If two triangles are similar, then the ratio of the area of both triangles is proportional to the square of the ratio of their corresponding sides.

Solution,

Using the Area of similar triangles theorem

→ ar ( smaller triangle ) / ar ( bigger triangle ) = ( side of smaller triangle )² / ( corresponding side of bigger triangle )²

→ 16 / 36 = (12)²/ (x)²

→ 8 / 18 = 144 / x²

→ 4 / 9 = 144 / x²

→ x² = 144 × 9 / 4

→ x² = 324

→ x = 18  cm

→

Therefore,

• Corresponding side of bigger triangle will be 18 cm.

Answer 2

Step-by-step explanation:

Given : -

• Area of the two similar triangles are 36 cm² and 16 cm².

• side of the smaller triangle is 12 cm

To Find : -

• find corresponding side of the bigger triangle. *

Solution : -

By using the theorem,

• When the two triangles are similar, then the ratio of there areas is equal to the ratio of the square of there corresponding sides.

∴ Area of the ΔABC/Area of the ΔPQR = AB²/PQ²

∴ 36 /16 = AB²/12²

⇒ AB² = 36 × 144/ 16

⇒ AB² = 36 × 9

⇒ AB² = 524 cm.

⇒ AB = √524

⇒ AB = 27

Hence, the corresponding side of the bigger triangle is 27 cm.