Use Lagrange multipliers to show that a triangle with perimeter p with the highest area is an equilateral triangle. (Hint: Use Heron's formula for the area of a triangle with perimenter p and side lengths a, b, c. The formula is attatched to the question)

Q: In quadrilateral ABCD (Figure 8.20), the lengths of the sides and of diagonal BD are shown. Find the…

A: Given: A quadrilateral ABCD Formula Used: Heron's Formula: s=a+b+c2Area=ss-as-bs-c

Q: Margaret has moved into an apartment and wants to make some inexpensive furniture and storage pieces…

A: Margaret has moved into an apartment and wants to make some inexpensive furniture and storage pieces…

Q: For the following questions, refer to the right triangle shown below: 3.0 m 4.0 m a) Determine the…

A: a) Given triangle is right  angle triangle. we know that in right angle triangle, square of…

Q: Given right triangle ABC with its right angle at vertex C. Let side BC = a, CA b, and AB c. Use…

A: Stewart's theorem provided the relation between the lengths of the sides of a triangle and the…

Q: 3. Find the perimeter of a right angled triangle with sides a = ₁ √3 cm and b = the hypotenuse. 2√3…

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Q: Connor decides to increase the number of sides of a random polygon so that the sum of its interior…

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Q: Since this is a 30-60-90 triangle, what should be the remaining leg length be? (Confirm your answer…

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Q: Consider a triangle whose shortest sides have lengths 9 and 12. The longest side of the triangle has…

A: As per question given triangle is right angle triangle  Longest side of right angle  triangle is…

Q: The triangle ABC is BC 6.3 cm and AC 7.5 cm. From a point D on AB, a transversal is drawn parallel…

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Q: Show use of trigonometry to determine the size of angle ZPRQ in the triangle below, where 2QPR =…

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Q: Before James Garfield was elected president of the United States, he discovered a proof of the…

A: Thank you 😊

Q: . Suppose you have to make a hexagonal box. Each side of the box has to be X (your student ID) cm…

A: Hexagon is a figure with six sides. A hexagonal box will have six sides and two faces up and down as…

Q: Find the area of a rhombus if its longer diagonal measures 18 ft. and the interior angle opposite of…

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Q: x 3+ (e) Let h = f+ 2g. Does lim h(x) exist? If so, find it. If not, explain why. x →3 (f) Is there…

A: We first give an example of a function f:R→R such that f satisfies all the give conditions and then…

Q: CONSTRUCT EQUILATERAL TRIANGLE UPON AB AS THE BASE. At

A: According to question given thatAB is the base of the equilateral triangle and we have to construct…

Q: In your own words summarize what the angles bisected by diagonal theorem says about parallelograms.…

A: Here we have to use own word to summarize What the angle bisected by diagonal theorem says about…

Q: Right Triangles and Pythagorean Theorem Classwork What is the longest stick that will fit inside a…

A: Here we have to find the length of the longest stick that can fit inside the given box. Here we use…

Q: Choose the correct definition of square among the following and explain why • A. A parallelogram…

A: A. A parallelogram with congruent sidesIf all the sides of a parallelogram are congruent or equal to…

Q: 10. Use the Pythagoras theorem to find the missing lengths of the following triangles. The theorem…

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Q: Suppose you have a regular hexagon like the one below in which the side lengths are all one unit. E…

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Q: Judith was supposed to draw a quadrilateral with two acute and two obtuse angles. Which figure below…

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Q: Can the sides of a triangle have length 0.7,1.1,and 1.8

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