Question

Perimeter of an isosceles trapezoid is $12\text{units}.$ Dimension of two adjacent sides are $3\text{units}$ and $4\text{units}.$ If all the sides have integer dimensions, find the possible dimensions of two parallel side.

• A. $1\text{unit}$
• B. $2\text{units}$
• C. $3\text{units}$
• D. $4\text{units}$

Answer 1

Answer: (A), (B), (C), (D)

$4\text{units}$

An isosceles trapezoid is formed by cutting an isosceles triangle along a line parallel to the side of the triangle connecting the equal angles of the triangle.

Here, $EDCB$ is the isoscele trapezoid wtih $EB=DC$ and $ED\ne BC$

Given: Perimeter $=12\text{units}.$
Dimension of two adjacent sides are $3\text{units}$ and $4\text{units}.$

Two such combinations are possible.

Hence, the possible dimension of both parallel sides are $1\text{unit},2\text{units},3\text{units}$ and $4\text{units}.$