A quadrilateral has two pair of opposite parallel sides. Each of one pair of parallel sides is 4 yards long. Each of the second pair of sides is 8 yards long. A diagonal connecting the opposite corners of the quadrilateral is 9 yards long. Is rectangle?

1 Answer
Mar 12, 2018

No. It is not a rectangle. See explanation.

Explanation:

To check if the quadrilateral is a rectangle we have to check if the triangles, to which the diagonal divides it are right angled. The sides of the triangles are #4#, #8# and #9# yards long.

To check if the triangle is right we use the Pytagorean Theorem.

We have to check if the square of the diagonal equals to the sum of squares of the sides.

Left side is:

#L=9^2=81#

Right side is:

#R=4^2+8^2=16+64=80#

Left side is different from the right, so the triangle is NOT right. This means that the quadrilateral is NOT a rectangle.