What are the dimensions

Question

Suppose the base and height of a triangle sum to 15, and the area of the triangle is 28 square cm. What are the dimensions (base and height) of the triangle?

 

Please help me solve and show the answer

Answer 1

Let x = the base

Let y = the height

 

 

Set up equations to represent the sum and the area.

 

x + y = 15             eq1

 

xy / 2 = 28

xy = 56                   eq2

 

 

We need to find two numbers that give a sum of 15 at the same time, give a product of 56. 

 

Two numbers that satisfy both conditions are 7 and 8.  This is because when you add them, you get 15.  When you multiply them, you get 56.

 

Therefore the base and height is 7 cm and 8 cm.  The order does not matter at all.