Question

Quadrilateral GOLD OL = 7.5 cm, GL = 6 cm, LD = 5 cm, DG = 5.5 cm and OD = 10 cm, Construct the quadrilateral with the measurements given.

Answer 1

Given: OL = 7.5 cm , GL = 6 cm , LD = 5 cm , DG = 5.5 cm and OD = 10 cm

To construct a Quadrilateral GOLD

By constructing a rough figure and marking given detail,

we find we are given 3 sides of quadrilateral i.e., GO , GD , DL and both diagonals .i.e., GL & OD . Also all sides of 2 triangles with common base GD i.e., Δ GOD & ΔGLD

Step-by-step  Construction:

Step 1: Draw a line segment GD of length 5.5 cm

Step 2: With G as center, draw an arc of radius 7.5 cm above Point G

Step 3: With D as center, draw an arc of radius 10 cm such that it intersect arc of step 2. Point of intersect of both arc is O.

Step 4: Join GO.

Step 5: With G as center, draw an arc of radius 6 cm above Point L

Step 6: With D as center, draw an arc of radius 5 cm such that it intersect arc of step 5. Point of intersect of both arc is Point L

Step 7: Join DL.

Step 8: Now, Join OL, we get the Required Quadrilateral GOLD

Answer 2

Step 1: Draw a line segment GD = 6 cm.

Step 2: With G as center, draw an arc of radius 6 cm above the point D.

Step 3: With D as center, draw an arc of radius 5 cm such that it intersect arc of step 2. The point of intersection of both arcs is L.

Step 4: Join GL, LD.

Step 5: With D as center, draw an arc of radius 10 cm above the point G.

Step 6: With L as center, draw an arc of radius 7.5 cm such that it intersect arc of step 5. The point of intersection of both arcs is point O.

Step 7: Join DO, LOGO.

Now, GOLD is the required quadrilateral.

(see in attachment)