The areas of two similar triangles are 169 cm² and 121 cm² respectively. If the longest side of the larger triangle is 26 cm, find the longest side of the smaller triangle.
Answers
SOLUTION :
Given: Area of two similar triangles is 169cm² and 121cm². The longest side of the larger triangle = 26 cm.
We know that the ratio of areas of two similar triangles is equal to the ratio of squares of their corresponding sides.
ar(larger∆)/ar(smaller ∆) = (side of the larger triangle/ side of the smaller triangle)²
169/121 = (side of the larger triangle/ side of the smaller triangle)²
On taking square root on both sides,
√169/121 = √(longest side of the larger triangle/ longest side of the smaller triangle)²
13/11 = longest side of the larger triangle/ longest side of the smaller triangle
13/11 = 26/longest side of the smaller triangle
longest Side of the smaller triangle = ( 11×26)/13 = 11 × 2 = 22 cm
longest Side of the smaller triangle = 22 cm
Hence, the longest side of the smaller triangle is 22 cm.
HOPE THIS ANSWER WILL HELP YOU....
Answer:
Step-by-step explanation:
Given: Area of two similar triangles is 169cm² and 121cm². The longest side of the larger triangle = 26 cm.
We know that the ratio of areas of two similar triangles is equal to the ratio of squares of their corresponding sides.
ar(larger∆)/ar(smaller ∆) = (side of the larger triangle/ side of the smaller triangle)²
169/121 = (side of the larger triangle/ side of the smaller triangle)²
On taking square root on both sides,
√169/121 = √(longest side of the larger triangle/ longest side of the smaller triangle)²
13/11 = longest side of the larger triangle/ longest side of the smaller triangle
13/11 = 26/longest side of the smaller triangle
longest Side of the smaller triangle = ( 11×26)/13 = 11 × 2 = 22 cm
longest Side of the smaller triangle = 22 cm
Hence, the longest side of the smaller triangle is 22 cm.
HOPE THIS ANSWER WILL HELP YOU....