Question

What is the value of x?

Answer 1

50.6 cm

Explanation:

Basic proportionality theorem:

If a line is drawn parallel to one side of a triangle intersecting the other two sides in distinct points, then the other two sides are divided in the same ratio.

`\sf (MA)/(AN)=(MB)/(BP)`

To find the value of MA, subtract 14 from 46.2.

MA = MN - AN

= 46.2 - 14

= 32.2 cm

To find the value of BP, subtract x from 72.6 cm.

BP = MP - MB

= 72.6 - x

`\sf (32.2)/(14)=(x)/(72.6-x)\\\\Simplify,\\\\2.3 =(x)/(72.6-x)`

Cross multiply,

2.3*(72.6 - x) = x

Use distributive property, a*(b - c) = a*b - a*c.

2.3 * 72.6 - 2.3*x = x

166.98 - 2.3x = x

Add 'x' to both sides,

166.98 = x + 2.3x

166.98 = 3.3x

Divide both sides by 3.3,

3.3x = 166.98

x = 166.98 ÷ 3.3

`\boxed{\bf x = 50.6 \ cm}`