Question

The area of a triangle is 80in^2. The ratio of the length of its base to its heights is 5:2. What are the base and height of the triangle?

Answer 1

Data:
H (height) and B (base)
Area = 80 in²

`(B)/(H) = (5)/(2)`

Knowing that the formula of the area of ​​a triangle:

`A = (B*H)/(2)`

Solving:
We isolate one of the terms (B or H) to find its values
Product of extremes equals product of means:

`(B)/(H) = (5)/(2)\to 2*B = 5*H\to 2B = 5H\to B = (5H)/(2)`

Now substitute in the formula the data found:

`A = (B*H)/(2)`

`80 = ( (5H)/(2) *H)/(2)`

`80*2 = (5H^2)/(2)`

`160 = (5H^2)/(2)`

`160*2 = 5H^2`

`320 = 5H^2`

`5H^2 = 320`

`H^2 = (320)/(5)`

`H^2 = 64`

`H = √(64)`

`\boxed{H = 8\:in}\longrightarrow\:\textbf{height} \end{array}}\qquad\quad\checkmark`

Now find the value of base (B), if:

`B = (5H)/(2)`
Soon:

`B = (5*8)/(2)`

`B = (40)/(2)`

`\boxed{B = 20\:in}\longrightarrow\:\textbf{base} \end{array}}\qquad\quad\checkmark`