Question

In the frame ABCD, AB = 12 inches, BC = 35 inches, CD = 12 inches, DA = 35 inches, BD = 37 inches, and AC = 37 inches, explain how the artist can be sure that the frame is rectangular. Draw a sketch to help you .

Answer 1

Answer with Step-by-step explanation:

We are given that a frame ABCD

AB=CD=12 in

BC=DA=35 in

AC=BD=37 in

We know that

In rectangle

Opposite sides are equal.

Diagonals are of equal length.

Each angle is 90 degrees.

Using the property

Opposite sides are equal in given ABCD frame and diagonals are equal in length.

ABCD is a parallelogram.

In triangle ABC

`AB^2+BC^2=(12)^2+(35)^2=1369`

`AC^2=(37)^2=1369`

`AC^2=AB^2+BC^2`

It satisfied Pythagoras theorem. Hence, triangle ABC is a right triangle.

Similarly, triangle BDC is a right triangle.

Angle B=Angle D(Opposite angles are equal in parallelogram)

Angle A=Angle C (Opposite angles are equal in parallelogram)

Angle A=Angle B=Angle C=Angle D=90 degrees

Hence, ABCD is a rectangle.