(imageshack)(.)us(/)photo (/) my-images (/)42(/)2vja. jpg(/)
Open that link please , just delete the parentheses please
please help me with my assignments
I beg you cooperate with me huhu
1. in the figure , the areas of traingle cef, triangle abe, triangle adf are 3,4, and 5 respectively. find the area of triangle aef
2. equialateral triangle abc has an area of square root of 3 and side of length 2. point p is an arbitrary point in the interioir of the traignle. what is the sum of the distances from p to ab, ab, and bc?
3. in the accompanying firgure , abcd is a square . suppose be=3 cm, ec=1cm and p is a point on the diagonal bd. find the smallest possible value of pe + pc in cm.
4. in triangle abc, ab=7, ac=9. on ab, point d is taken so that bd = 3. de is drawn cutting ac in e so that quadrilateral bced has 5/7 the area of trangile abc. find ce.
5. find the ratio between the area of a square inscribed in a circle and an equilateral circumscribed about the same circle.
I did #5 for you on Thursday.
http://www.jiskha.com/display.cgi?id=1383829501
Did you not look at it ?
for the above, it says" your image has been removed"
What about the triangle ? uhm. . . no triangle there..
I apologize, but as an AI text-based bot, I am not able to directly open or view links or images. However, I can still assist you with solving the problems you mentioned using the given information. Let's go through each question step by step:
1. To find the area of triangle AEF, you can consider the fact that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding side lengths. In this case, triangles CEF, ABE, and ADF are similar to triangle AEF. Let's assume the side lengths of triangle AEF are a, b, and c. Then we have:
Area(CEF) / Area(AEF) = (CE / AE)^2 = 3
Area(ABE) / Area(AEF) = (AB / AE)^2 = 4
Area(ADF) / Area(AEF) = (AD / AE)^2 = 5
Based on these ratios, you can set up a system of equations to solve for the side lengths. From the second equation, you can find the length of AE in terms of AB. Substituting this into the other equations will help you solve for the side lengths a, b, and c. With those side lengths, you can use Heron's formula to calculate the area of triangle AEF.
2. To find the sum of the distances from point P to AB, AC, and BC in an equilateral triangle ABC, we can make use of the fact that the distances from an arbitrary point in the interior of an equilateral triangle to its sides are proportional to the lengths of those sides.
Let's assume the side length of triangle ABC is s. The sum of the distances from point P to AB, AC, and BC is then:
Sum = (s/3) + (2s/3) + (s/3) = 2s
So, the sum of the distances from point P to AB, AC, and BC is equal to twice the side length of the equilateral triangle.
3. In order to find the smallest possible value of PE + PC in question 3, we need to determine the location of point P on the diagonal BD that minimizes the sum of the distances PE and PC.
Based on the given information and the fact that ABCD is a square, we can conclude that triangles BEC and PEC are similar. This means that the ratio of their corresponding side lengths is equal to the ratio of their corresponding heights.
Using this, along with the given measurements of BE and EC, we can express the lengths of PE and PC in terms of x:
PE = (BE / EC) * x = (3 / 1) * x = 3x
PC = ((EC + BE) / EC) * x = (4 / 1) * x = 4x
The sum of PE and PC is then: PE + PC = 3x + 4x = 7x
To minimize the sum of PE and PC, we need to minimize the value of x. Since x represents a distance, the smallest possible value for x is zero. Therefore, the smallest possible value of PE + PC is 7(0) = 0 cm.
4. To find the length of CE in question 4, we need to use the given information about the areas of quadrilateral BCED and triangle ABC.
Let's assume that CE = x. Since the quadrilateral BCED has 5/7 the area of triangle ABC, the ratio of their areas is (5/7). Therefore, we have:
Area(BCED) / Area(ABC) = (CE / AC) * (BD / AB) = (5/7)
Substituting the given values, we get:
(x / 9) * (3 / 7) = (5/7)
Simplifying this equation will help you solve for the length of CE.
5. To find the ratio between the area of a square inscribed in a circle and an equilateral triangle circumscribed about the same circle, we can maximize the use of geometric properties.
Let's assume the radius of the circle is r. The diagonal of the square (which is also the diameter of the circle) can be found using the Pythagorean theorem, and it will be equal to 2r. The side length of the square will be √2 * (side length of the equilateral triangle).
The area of the square is side length^2, and the area of the equilateral triangle is (side length^2 * √3) / 4.
By solving the respective expressions for the areas of the square and the equilateral triangle, you can find their ratio.
I hope these explanations help you understand how to approach and solve the given problems.