Question

Areas of two similar triangles are 36 cm^2 and 100 cm^2. If the length of a side of the larger triangle is 20 cm, then the length of the corresponding side of the smaller triangle is:​

Answer 1

Answer :

12 cm

Solution :

Given,

Areas of two similar triangles,

ar(∆ABC) = 36 cm²

ar(∆DEF) = 100 cm²

Side of larger triangle, DE = 20 cm

Let, side of smaller triangle be 'x' cm.

We know that,

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.

⟶ ar(∆DEF)/ar(∆ABC) = (DE/AB)²

⟶ 100/36 = (20/x)²

⟶ 100/(36×400) = 1/x²

⟶ x² = 4 × 36

⟶ x = √144

⟶ x = 12 cm

∴ Side of smaller triangle = 12 cm

Answer 2

Step-by-step explanation:

Perimeter of trapezium = 104 m

Length of Non-parallel sides = 18 m and 22 m

Altitude = 16m

Area of Trapezium = 0.5 * (sum of parallel sides)*altitude ------ (1)

Sum of parallel sides = Perimeter - (sum of non-parallel sides) = 104 m - (18+22)m = 104-40 m = 64 m

From (1), Area of Trapezium = 0.5*64*16 = 512 m^2

Ans: Area of trapezium = 512 m^2