Answer:
[tex]y = 36[/tex]
Step-by-step explanation:
Given; the triangle above
Required
Find y
This question falls under the topic/subtopic similar triangles where we need to make comparison between similar sides'
But first, it should be noted that triangle MOP is similar to triangle MLN
This implies that
Side MP is similar to MN
Side MO is similar to ML
Mathematically; This can be represented as follows;
[tex]\frac{MP}{MN} = \frac{MO}{ML}[/tex]
Where MP =y; MN = y + 18; MO = 28; ML = 28 + 14
Substitute these values in the above expression
[tex]\frac{y}{y+18} = \frac{28}{28+14}[/tex]
[tex]\frac{y}{y+18} = \frac{28}{42}[/tex]
Multiply both sides by 42
[tex]42 * \frac{y}{y+18} = \frac{28}{42} * 42[/tex]
[tex]\frac{42y}{y+18} = \frac{28*42}{42}[/tex]
[tex]\frac{42y}{y+18} = 28[/tex]
Multiply both sides by y + 18
[tex](y+18)*\frac{42y}{y+18} = 28 * (y+18)[/tex]
[tex]42y = 28 * (y+18)[/tex]
Open Bracket
[tex]42y = 28 * y+28 * 18[/tex]
[tex]42y = 28y+504[/tex]
Subtract 28y from both sides
[tex]42y - 28y = 28y - 28y +504[/tex]
[tex]14y = 504[/tex]
Divide both sides by 14
[tex]\frac{14y}{14} = \frac{504}{14}[/tex]
[tex]y = \frac{504}{14}[/tex]
[tex]y = 36[/tex]
