In an isosceles triangle with a base of 7 cm, a segment is drawn connecting the midpoints of the lateral sides.

| December 13, 2020 | education

In an isosceles triangle with a base of 7 cm, a segment is drawn connecting the midpoints of the lateral sides. Determine the type of the resulting quadrilateral and find its perimeter if the sides of the triangle are 16 cm.

The segment connecting the midpoints of the sides of the triangle is a midline parallel to the base and equal to half of the base.
Since the sides are equal and divided by the middle line in half, the sides of the resulting quadrilateral are equal. It follows from everything that a quadrilateral is an isosceles trapezoid.
The sides of the trapezoid are two times smaller than the sides of the triangle, which means they are equal to 16/2 = 8 (cm). The middle line is 2 times smaller than the base, which means that it is equal to 7/2 = 3.5 (cm).
Perimeter – the sum of the lengths of all sides = 8 + 8 + 7 + 3.5 = 26.5 (cm).
Answer: an isosceles trapezoid with a perimeter of 26.5 cm.



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