The areas of two similar triangles are 144cm square and 81cm square. If one side of the first triangle is 6cm, what is the length of the corresponding side of the second?
if the sides are in ratio r, the areas are in the ratio r^2.
So, the sides are in the ratio 12:9
4x6=24/3=8
To find the length of the corresponding side of the second triangle, we can use the concept of ratios.
First, let's find the ratio between the areas of the two triangles. The ratio of the areas of similar figures is equal to the square of the ratio of their corresponding sides.
In this case, the ratio of the areas is given as (144 cm^2) : (81 cm^2). To simplify, we can divide both values by the greatest common divisor, which is 9.
So, the simplified ratio of the areas is (16 cm^2) : (9 cm^2).
Next, since the ratio of the areas is equal to the square of the ratio of the sides, we can take the square root of the ratio of the areas to find the ratio of the sides.
√[(16 cm^2) : (9 cm^2)] = (4 cm) : (3 cm)
This means that the corresponding sides of the two triangles have a ratio of 4 cm to 3 cm.
Finally, since we know that one side of the first triangle is 6 cm, we can use this information to find the length of the corresponding side of the second triangle.
We can set up the following proportion:
(6 cm) : (x cm) = (4 cm) : (3 cm)
By cross-multiplying, we get:
(6 cm) * (3 cm) = (4 cm) * (x cm)
18 cm^2 = 4 cm * x cm
To solve for x, divide both sides of the equation by 4 cm:
18 cm^2 / 4 cm = x cm
4.5 cm = x
Therefore, the length of the corresponding side in the second triangle is 4.5 cm.