The areas Of Two Similar Triangle Are 144cm & 81cm . If One Of The First Triangle 6cm, What Is The Legth Of The Correspoding Side Of The Secod?
Any reason why you are capitalizing every word?
Assuming your garbled last sentence is something like:
"If one of the sides of the first triangle is 6 cm, what is the length of the corresponding side of the second triangle ? "
Areas of similar triangles are proportional to the square of their corresponding sides, so
6^2/x^2 = 144/81
take the square root of both sides:
6/x = 12/9
12x = 54
x = 54/12 = 9/2
the corresponding side is 4.5 cm
9/2
To find the corresponding side of the second triangle, we can use the concept of similarity. The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.
Given that the area of the first triangle is 144 cm² and one of its corresponding sides is 6 cm, we can set up the following proportion:
(Length of corresponding side of second triangle)² / 6² = 81 cm² / 144 cm²
Simplifying the equation, we have:
(Length of corresponding side of second triangle)² / 36 = 81 / 144
Cross-multiplying:
(Length of corresponding side of second triangle)² = (81 / 144) * 36
(Length of corresponding side of second triangle)² = 0.5625 * 36
(Length of corresponding side of second triangle)² = 20.25
Taking the square root of both sides, we get:
Length of corresponding side of second triangle ≈ √20.25
Length of corresponding side of second triangle ≈ 4.5 cm
Therefore, the length of the corresponding side of the second triangle is approximately 4.5 cm.
To find the length of the corresponding side of the second triangle, we can use the property of similarity between two triangles. The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding side lengths.
Let's assume the corresponding side length of the second triangle is "x". We are given that the area of the first triangle is 144 cm² and the corresponding side length is 6 cm. We are also given that the area of the second triangle is 81 cm².
Now, let's set up the proportion to find the ratio of the side lengths:
(6/x)² = 144/81
Simplifying the equation:
36/x² = 144/81
Cross multiplying:
36 * 81 = 144 * x²
Using a calculator:
2916 = 144 * x²
Dividing both sides by 144:
2916/144 = x²
20.25 = x²
Taking the square root of both sides:
x = √20.25
x ≈ 4.5 cm
Therefore, the length of the corresponding side of the second triangle is approximately 4.5 cm