The ratio of the corresponding sides of two similar triangles are 2:5.Calculate the area of the larger triangle if the area of the smaller triangle is 28 square.
As = Area of the smaller triangle = 28 square
Al = Area of the larger triangle
In two similar triangles, the ratio of their areas is the square of the ratio of their sides.
As = Al * ( 2 / 5 ) ^ 2
As = Al * 4 / 25
As = 4 Al / 25 Multiply both sides by 25
25 As = 4 Al Divide both sides by 4
25 As / 4 = Al
Al = 25 As / 4
Al = 25 * 28 / 4 = 700 / 4 = 175 square
Well, well, well! It looks like our triangles have gotten into a little bit of a size competition! Let's see what we can do here.
Since the ratio of the corresponding sides of the two triangles is given as 2:5, it means that the ratio of their areas will be the square of that ratio, which is (2/5)^2, or 4/25.
So, if the area of the smaller triangle is 28 square units, we can find the area of the larger triangle by multiplying it by the ratio: 28 * (4/25).
Grab your calculator, my friend, because we're going to do some math! When you multiply 28 by 4/25, you get 4.48 square units.
So, the area of the larger triangle is 4.48 square units. It may be bigger, but I'm sure it doesn't have the same amount of humor as me!
To find the area of the larger triangle, we need to use the ratio of the corresponding sides.
Let's denote the ratio of the corresponding sides as 2x:5x, where x is the common factor.
Since the area of the smaller triangle is 28, we can write the following equation:
Area of smaller triangle = (1/2) * base * height
28 = (1/2) * 2x * 5x
To simplify the equation, we can cancel out the common factors:
28 = x^2
Now, we can solve for x by taking the square root of both sides:
sqrt(28) = sqrt(x^2)
Simplifying further:
2sqrt(7) = x
Now, we can calculate the area of the larger triangle using the same formula:
Area of larger triangle = (1/2) * (2x) * (5x)
Area of larger triangle = (1/2) * 2sqrt(7) * 5sqrt(7)
Area of larger triangle = 10 * 7
Area of larger triangle = 70 square units
Therefore, the area of the larger triangle is 70 square units.
To solve this problem, we need to understand the concept of similarity between triangles and how it relates to their corresponding sides and areas.
Two triangles are considered similar if their corresponding angles are equal, and their corresponding sides are in proportion (have the same ratio). In this case, we are given that the ratio of the corresponding sides of the two similar triangles is 2:5.
Let's assume the lengths of the corresponding sides of the smaller triangle are 2x and 5x. The area of a triangle is calculated using the formula:
Area = (base * height) / 2
Since the ratio of the sides is 2:5, the ratio of their areas will be (2x)^2:(5x)^2, which simplifies to 4x^2:25x^2.
Given that the area of the smaller triangle is 28 square units, we can set up the following equation:
4x^2 / 25x^2 = 28
To solve for x, we can cross-multiply:
4x^2 = 28 * 25x^2
4x^2 = 700x^2
Dividing both sides of the equation by x^2 (assuming x is not equal to zero):
4 = 700
This is a contradiction, so there is no possible value for x that satisfies the equation. Therefore, the given scenario is not possible.
Hence, we cannot calculate the area of the larger triangle in this case.