Question

the length of base and altitude of triangle is 32cm and 18cm respectively. if the area of a square is double than this triangle, find the length of a square
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Answer 1

Length of the square = 12 cm.

• In a two-dimensional plane, a triangle's area is the area that it completely encloses. A triangle is a closed shape with three sides and three vertices, as is common knowledge. The entire area occupied by a triangle's three sides is referred to as its area. Half of the product of the triangle's base and height provides the general formula for calculating the area of the triangle.
• Generally speaking, a "area" is the area included within the perimeter of a flat object or figure. Measurements are made in square units, with square metres serving as the reference unit .There are predefined formulas for the computation of area for squares, rectangles, circles, triangles, etc.

Here, according to the given information, it is given that, the length of base and altitude of triangle is 32cm and 18cm respectively.

Now, we know that, area of a triangle is equal to $\frac{base. altitude}{2}$= $\frac{32.18}{2} = 288$cm².

Now, the area of a square is double than this triangle.

Then, area of the square = $\frac{288}{2}= 144$ cm².

Then, length of the square = 12 cm.

Hence, length of the square = 12 cm.

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Answer 2

Answer:

Length of the square is 24 cm.

Explanation:

What is a Triangle and Square ?

A triangle is a three-sided polygon in geometry that has three edges and three vertices. The most significant feature of a triangle is that the total of the interior angles of a triangle is equal to 180 degrees. This characteristic is known as the triangle's angle sum property.

A triangle's area is the area that it takes up in two dimensions. Depending on their size, distinct triangles have varying areas from one another. If we are aware of a triangle's base and height, we can determine its area. It has a square unit of measurement.

A square is one of numerous forms that belong to the quadrilateral family. A parallelogram, rectangle, and rhombus are all examples of squares. Due to its two pairs of parallel, congruent sides, it is a parallelogram. It is a rectangle because it contains four congruent internal angles and two sets of parallel, congruent sides. It has four sides that are identical, which makes it a rhombus.

The linear measurement of area is always stated in square units. Area is often defined as length times width, although in a square, length equals width.

Length of Base in Triangle = 32 cm

Height or Altitude of the triangle = 18cm

Area of the triangle = $\frac{1}{2}*Base*Height$ = $\frac{1}{2}*32*18 = 288 \ cm^{2}$.

Area of the Square = 2 * Area of Triangle = 2 *288 = 576 $\ cm^{2}$

Length of each side of the Square = $\sqrt[]{576} = 24 \ cm$        

 [∵ Area of Square = $(lengths)^{2}$ ]

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