Bissoy.com
Doctors Medicines MCQs Q&A

A flexible wire is used to make triangles. When this wire is folded from its middle, a triangle of 9 cm perimeter can be formed. If an equilateral triangle is formed with the given length of the wire such that it has the maximum possible perimeter, what is the area of triangle formed?

A flexible wire is used to make triangles. When this wire is folded from its middle, a triangle of 9 cm perimeter can be formed. If an equilateral triangle is formed with the given length of the wire such that it has the maximum possible perimeter, what is the area of triangle formed? Correct Answer 15.57 cm<sup>2</sup>

Let the length of wire is L

The wire is folded from its middle then the perimeter is half of the length of the wire,

⇒ L/2 = 9 cm

⇒ L = 18 cm

The largest equilateral triangle that can be formed using this length of wire is a triangle which has each side of 6 cm

∴ Area of an equilateral is ((√3)/4) × side2 = (1.73 × 36)/4 = 1.73 × 9 = 15.57 cm2

Related Questions

Suppose chords AB and CD of a circle intersect at a point P inside the circle. Two right-angled triangles A’P’B’ and C’Q’D’ are formed as shown in the figure below such that A’P’ = AP, B’P’ = BP, C’Q’ = CP, D’Q’ = DP and ∠A’P’B’ = 90° = ∠C’Q’D’. Which of the following statements are not correct? 1. A’P’B’ and C’Q’D’ are similar triangles, but need not be congruent 2. A’P’B’ and C’Q’D’ are congruent triangles. 3. A’P’B’ and C’Q’D’ are triangles of same area. 4. A’P’B’ and C’Q’D’ are triangles of same perimeter. Select the correct answer using the code given below.
In an equilateral triangle, another equilateral triangle is drawn inside joining the mid-points of the sides of the given equilateral triangle and the process continues uptofive times. What is the ratio of the area of fourth triangle to that of sixth triangle? (Original triangle is counted as 1st triangle)
A circle of maximum area is inscribed in the square. An equilateral triangle is inscribed in that circle and all the vertices of the triangle touch the circle. A triangle is formed by the joining of the midpoint of the sides of the equilateral triangle. Find the ratio of the area of the square and area of the triangle which is formed by midpoints.
To make a puzzle piece, a cardboard block of dimensions 9 cm × 5 cm is cut along the dotted lines as shown below. Each semicircle cut from the length of the cardboard have an area of 2π cm2, while each semicircle cut from the breadth of the cardboard have an area of π/2 cm2. If the four triangles cut from the corners are equilateral triangles, each having an area of √3/4 cm2, then find the perimeter of the puzzle piece so formed?
In an equilateral triangle, another equilateral triangle is drawn inside joining the mid-points of the sides of the given equilateral triangle and the process continues up to seven times. What is the ratio of the area of fourth triangle to that of seventh triangle?
Select three out of five combination of the parts 1, 2, 3, 4 and 5 which can fit into each other to form an equilateral triangle.
Construction of Squares and Triangles mcq question image
Select three out of five combination of the parts 1, 2, 3, 4 and 5 which can fit into each other to form an equilateral triangle.
Construction of Squares and Triangles mcq question image
Select three out of five combination of the parts 1, 2, 3, 4 and 5 which can fit into each other to form an equilateral triangle.
Construction of Squares and Triangles mcq question image
Select three out of five combination of the parts 1, 2, 3, 4 and 5 which can fit into each other to form an equilateral triangle.
Construction of Squares and Triangles mcq question image
Select three out of five combination of the parts 1, 2, 3, 4 and 5 which can fit into each other to form an equilateral triangle.
Construction of Squares and Triangles mcq question image