Question

$△$XYZ is constructed such that XY = 4 cm, XZ = 8 cm and $\angle$X = 20${}^{\circ }$. Then the difference between the lengths of sides YZ and XY is equal to

• A. 0.5 cm
• B. 1.5 cm
• C. 2.5 cm
• D. 3.5 cm

Answer 1

The correct option is A

0.5 cm

Step 1:
Draw the base line XY of the length 4 cm.

Step 2:
Measure the angle X with your protractor. Make a mark at 20 degrees and draw a line from X passing through the mark.

Step 3:
Cut an arc of radius 8 cm on the line passing through the point X. The point where this arc cuts the line is the point Z.

Step 4:
Draw a line from Y to point Z, to get the required triangle XYZ, as shown below.

From the above construction, we see that the length of side YZ is 4.5 cm.

Now, the difference between the lengths of sides YZ and XY is equal to 0.5 cm(= 4.5 cm - 4 cm).