he perimeters of two similar triangles are 26 cm and 39 cm. The ratio of their areas will be
Question
he perimeters of two similar triangles are 26 cm and 39 cm. The ratio of their areas will be
Solution
The ratio of the areas of two similar triangles is the square of the ratio of their corresponding sides. The ratio of their perimeters is the same as the ratio of their corresponding sides.
Here, the ratio of the perimeters of the two triangles is 26:39.
To simplify this ratio, we divide both numbers by their greatest common divisor, which is 13.
So, the simplified ratio is 2:3.
Therefore, the ratio of their areas will be the square of this ratio, which is (2^2):(3^2) = 4:9.
Similar Questions
The ratio of the side lengths of 2 similar triangles is 3:5. The smaller triangle has sides that measure 5 centimeters, 7 centimeters, and 9 centimeters. What is the perimeter, in centimeters, of the larger triangle?Responses1235123512 and 3 fifths212121353535636363105
Refer to the sketch above. The area of the right triangle is 60 cm22. If its height is 12 cm long, its perimeter isA.38,7 cmB. 37,6 cmC.36,6 cmD.37 cm
The lengths of the sides of a triangle are in the ratios 2 : 6 : 7The length of the longest side of the triangle is 24.5 cm.Work out the perimeter of the triangle.
The areas of two similar triangles are 81 cm2 and 49 cm2 respectively, then the ratio of their corresponding medians is
2. The ratio of the perimeters of two similar triangles is 3/5. The scale factor is ________
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.