Question

Triangles △ABC and △DFG are similar. The lengths of the two corresponding sides are 1.4m , and 56 cm. What is the ratio of the perimeters of these triangles ?

Answer 1

5:2

Explanation:

We have been given that triangles △ABC and △DFG are similar. The lengths of the two corresponding sides are 1.4 m and 56 cm.

Since both triangles are similar, therefore all corresponding sides will have same proportion.

Let us find proportion of corresponding sides of both triangles.

1 meter = 100 centimeter

1.4 meter = 1.4* 100 centimeters = 140 centimeters.

`\frac{\text{Side of triangle ABC}}{\text{Side of triangle DFG}}=(140)/(56)`

`\frac{\text{Side of triangle ABC}}{\text{Side of triangle DFG}}=(5)/(2)`

The ratio of sides of △ABC to sides of△DFG is 5:2.

Since perimeter of a triangle is sum of lengths of three sides of the triangle and all sides of both triangle have the ratio 5:2, therefore, their perimeters will be in same ratio, that is 5:2.

Answer 2

5/2

Explanation:

The ratio of perimeters is the same as the ratio of corresponding sides:

... (140 cm)/(56 cm) = 5/2