Question

Two triangles aresimilar.The length of a side of one of the triangle is 6times that of the corresponding sides of the other.Find the ratio of the perimeter and the area of the triangle

Answer 1

Answer:

$Ratio = 1 : 6$ --- of perimeters

$Ratio = 1: 36$ --- of areas

Step-by-step explanation:

Given

Represent the sides of the first triangle with x, y and z

The sides of the second triangle will be 6x, 6y and 6z

Solving (a): Ratio of perimeter.

The perimeter of the first is:

$P_1 = x + y + z$

The perimeter of the second is:

$P_2 = 6x +6 y + 6z$

Factorize:

$P_2 = 6(x +y + z)$

The ratio is:

$R = P_1 : P_2$

$R = x + y + z : 6(x + y + z)$

Cancel out x + y + z

$Ratio = 1 : 6$

Solving (a): Ratio of Areas.

If the height of the first is h and the base is b.

The height of the second will be 6h and the base, 6b.

The area of the first is:

$A_1 = 0.5 * b * h$

$A_1 = 0.5bh$

The area of the second is:

$A_2 = 0.5 * 6b * 6h$

$A_2 = 18b h$

The ratio is:

$Ratio = A_1 : A_2$

$Ratio = 0.5bh : 18bh$

Divide by 0.5bh

$Ratio = 1: 36$