the midpoints of the sides of a triangle with area $a$ are joined to form a triangle with area $m$. what is the ratio of $m$ to $t$? express your answer as a common fraction.

Respuesta :

While the midpoints of a sides of a rectangle having area $a$ are united to produce a triangle with size $m$, the area of a new triangle equals $frac14$ the area of a original triangle.

What does the word "area" mean?

A "area" is the size or length of an a double surface, which is frequently measured in square units. It is employed to describe a shape's or object's size, such as the length, width, or height of a side, a bit of land, or even a geometrical figure. By dividing a form's length by its breadth, the area of the form may be calculated. For instance, a rectangle with dimensions of 5 units in length and 3 units in width has a surface area of 15 square units. The area of a circle is calculated using the formula r2, wherein r is the ring's radius. A fundamental geometric concept known as "area" has several applications in the sectors of construction, real estate, and horticulture.

How to fix?

Assume that the original triangle has sides that are s1, s2, and s3. The triangle's area when the side's midpoints are united is [m=frac s 1s 2s 3 16]. This happens because the new triangle's area is $frac14$ the size of a original triangle since each side of a new triangle being half as long as the equivalent side of the old triangle.

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