Mathematics
The ratio between the areas of two similar triangles is 16 : 25. State the ratio between their :
(i) perimeters
(ii) corresponding altitudes
(iii) corresponding medians.
Similarity
13 Likes
Answer
We know that,
The ratio between the areas of two similar triangles is same as the square of the ratio between their corresponding sides.
Given,
Ratio between areas = 16 : 25.
So, ratio between sides = = 4 : 5.
(i) The ratio between the perimeters of two similar triangles is same as the ratio between their sides.
Hence, the required ratio = 4 : 5.
(ii) The ratio between the altitudes of two similar triangles is same as the ratio between their sides.
Hence, the required ratio = 4 : 5.
(iii) The ratio between the medians of two similar triangles is same as the ratio between their sides.
Hence, the required ratio = 4 : 5.
Answered By
4 Likes
Related Questions
The two similar triangles are equal in area. Prove that the triangles are congruent.
The ratio between the altitudes of two similar triangles is 3 : 5; write the ratio between their:
(i) corresponding medians.
(ii) perimeters.
(iii) areas.
On a map, drawn to a scale of 1 : 20000, a rectangular plot of land ABCD has AB = 24 cm and BC = 32 cm. Calculate :
(i) the diagonal distance of the plot in kilometre.
(ii) the area of the plot in sq. km.
The dimensions of the model of a multistoreyed building are 1 m by 60 cm by 1.20 m. If the scale factor is 1 : 50, find the actual dimensions of the building.
Also, find :
(i) the floor area of a room of the building, if the floor area of the corresponding room in the model is 50 sq. cm.
(ii) the space (volume) inside a room of the model, if the space inside the corresponding room of the building is 90 m3.