Question

Q3. Construct a rectangle of sides 50 mm and 70mm. i. Measure and write down the length of each diagonal. ii. Construct an angle bisector of ∠ .

Answer 1

Please have a look at the attachments to see the constructionof the rectangle and it's diagonal, bisector.

Construction of a triangle with length = 50mm and breadth = 70mm :

• We know that, 10 mm = 1 cm.

• Take a scale and draw 5 cms line segment, name it as AB.

• Now, take a protractor and make an angle of 90 degree marks on both ends.

• Draw line segments of 70mm or 7cm from the ends of A, B to their respective side 90 degree plotted points, through 90 degree points.

• Mark the end points of new line segments as C and D, such that AD and BC will be the new line segments of 70mm breadth.

• Join CD.

There forms a rectangle of length 50mm and breadth 70mm.

Measure and write down the length of each diagonal.

• In rectangle, lengths of both diagonals are same. So, finding one will be enough.

• In this rectangle ABCD, diagonals are AC and BD.

• On joining them and measuring their length, it is found that their length is of 86.02 mm or 8.602 cm.

• As rectangle's have right angles (90 degrees), You can measure the diagonal's length theoritically using hypotenuse BD² = AB² + AD² (You can go with any diagonal and their respective right angled triangles).

       So, diagonal BD² = 50² + 70²

                             BD = √(2500+4900) = 86.02 mm.

As length of the diagonal BD is 86.02 mm, length of the diagonal AC will also be 86.02 mm, or 8.206 cm.

Constructing an angular bisector :

• As any angle in a rectangle will be a right angle, on bisecting, the bisector makes the angle into two halves, 45 degrees each.

• For drawing a bisector, take 1 cm or 2 cm of length using compass, and draw two arcs from any of the vertex point to its adjacent sides.

• Then, from those 2 arc-ed points, draw an individual arc from each point, in opposite side diagonally.

• Mark a point where the two arcs meet and draw a line from the vertex you chose before to draw the arcs, to the arcs meeting point.

• The line you have drawn now is the angular bisector, that bisectsthe angle.

Learn more :

1) The sides of the rectangle are in the ratio 2:three and perimeter is 20cm draw the rectangle

https://brainly.in/question/6475025

2) Draw a rectangle AB=6cm and BD=8cm

https://brainly.in/question/6908802