Question

Areas of 2 simular s are 225cm square and81cm square. If side of smaller is 12 cm then find the corresponding side of another

Answer 1

let the two similar triangles are triangle ABC and triangle POR.
the two triangles are similar ---------------- (given)
therefore , by theorem on equal ratios ;
A (triangle ABC) / A (triangle PQR) = AB / PQ
therefore ;
A (triangle ABC) / A (triangle PQR) = 225 / 81
therefore ;
225 / 81 = AB / 12
therefore ;
AB Square =225 * (12 square) / 81
Therefore ;
AB = 15 * 12 / 9 ----------- Taking square root of both sides.
therefore ;
AB = 20 cm.
therefore corresponding side of the bigger triangle is 20 cm.

Answer 2

ATQ, the area of 2 similar triangle is 225cm² and 81cm² respectively. and the side of the smaller triangle is 12cm.

we have to find the corresponding side of the larger triangle.

let the smaller side of the triangle be x and y for the larger one.

now, we know that the square of ratio between corresponding sides of two similar triangles is equal to the ratio between their areas.

➡ 225cm²/81cm² = (y/x)²

➡ √225cm²/√81cm² = y/12

➡ 15/9 = y/12

➡ 15 × 12 = 9y

➡180 = 9y

➡ 180/9 = y

➡ y = 20cm

hence, the corresponding side of the larger triangle is 20cm.