Question

In the figure shown, XY is parallel to BC. What is the length of AX?

Answer 1

using Triangle parallel theorem

=> AX/XB = AY/YC

=> AX/8 = 7/10

=> AX = 56/10

=> AX = 5.6 unit

Hope it may help you.

Answer 2

Given:

Two triangles ABC and AXY are given whose side XY is parallel to BC.

To Find:

What is the length of AX?

Step-by-step explanation:

• In the given triangle AXY and ABC, side XY of triangle AXY and side BC of triangle ABC are parallel to each other.

       $So,$    $\angle AXY = \angle ABC$

                $\angle AYX=\angle ACB$

       

• As angle A is common in both the triangle ABC and AXY.

                    $\angle A= \angle A \textrm { (same)}$

• So, triangle ABC and AXY are similar.

       ΔAXY ≅ ΔABC.

• For two similar triangles, the ratio of any two corresponding sides is always the same.

• As both the triangle ABC and AXY are equal, the ratio of any two corresponding sides is always equal.

                      $\frac{AX}{XB} =\frac{AY}{YC}$

                      $\frac{AX}{8} =\frac{7}{10}$

                     $AX=\frac{56}{10}$

                     $AX=5.6 units$

So, the length of the side AX is 5.6 units.