THE RATIO OF THE PERIMETERS OF TWO SIMILAR TRIANGLES IS 1:3. htE AREA OF THE LARGER TRIANGLE IS 27FT^2. WHAT IS THE AREA OF THE SMALLER TRIANGLE.
SORRY FOR THE CAPITAL LOCK. MY COMPUTER KEPBOARD WILL NOT PUT IT TO LOWER CASE SORRY AGAIN.
No problem! To find the area of the smaller triangle, we can use the fact that the ratio of the areas of similar triangles is equal to the square of the ratio of their corresponding side lengths.
In this case, since the ratio of the perimeters is 1:3, we can also assume that the ratio of the corresponding side lengths is 1:3.
Let's say the corresponding side lengths of the smaller triangle to the larger triangle are x and 3x respectively. Since the area is proportional to the square of the side lengths, the area of the smaller triangle would be (x^2)/(3^2) = (x^2)/9.
We are given that the area of the larger triangle is 27 ft^2, so we can set up the equation:
(x^2)/9 = 27.
To solve for x, we can multiply both sides of the equation by 9:
x^2 = 243.
Taking the square root of both sides, we get:
x = √243.
Simplifying this, we find:
x ≈ 15.588 ft.
Now we can substitute this value of x back into the equation for the area of the smaller triangle:
Area of smaller triangle = (15.588^2)/9 ≈ 27.375 ft^2.
Therefore, the area of the smaller triangle is approximately 27.375 ft^2.
No problem! I can help you solve the problem. To find the area of the smaller triangle, we'll need to use the ratio of the areas of the triangles.
First, let's focus on the ratio of the perimeters of the triangles. The ratio is 1:3, which means that the lengths of the corresponding sides of the two triangles are in the same ratio. This implies that the lengths of the corresponding sides are in the ratio 1:3.
Next, let's turn our attention to the ratio of the areas of the triangles. The area of a triangle is given by the formula: Area = (base * height) / 2.
Since the corresponding sides of the two triangles are in the ratio 1:3, the ratio of their areas will be the square of that ratio, which is 1^2:3^2, or 1:9.
Given that the area of the larger triangle is 27 ft^2, we can set up the following equation:
Area of larger triangle / Area of smaller triangle = 27 / Area of smaller triangle = 1 / 9
To find the area of the smaller triangle, we can cross-multiply the equation:
27 = (1/9) * Area of smaller triangle
Now, we can solve for the Area of the smaller triangle:
Area of smaller triangle = (27 * 9) / 1 = 243 / 1 = 243 ft^2
Therefore, the area of the smaller triangle is 243 square feet.
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Answer:
the ratio of areas of two similar figures is the square of the ratio of the linear measures (in this case 1:3).