Question

The bases and height of these three right triangles (i don't have the pictures up but they are triangles) are in the same proportional relationship to each other

7 1/2 9, 10 1/4 12 3/10, 16 3/4 20 1/10,
what is the constant of proportionality?

Answer 1

The constant of proportionality is
`k=(6)/(5)`

Explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form
`k=(y)/(x)` or
`y=kx`

Let

x ----> the base of triangle

y ----> the height of triangle

To find out the constant of proportionality, divide the height by the base

First case

`x=7(1)/(2)=(7*2+1)/(2)=(15)/(2)`

`y=9`

`k=(y)/(x)`

substitute

`k=9:(15)/(2)=(18)/(15)`

Simplify

`k=(6)/(5)`

Second case

`x=10(1)/(4)=(10*4+1)/(4)=(41)/(4)`

`y=12(3)/(10)=(12*10+3)/(10)=(123)/(10)`

`k=(y)/(x)`

substitute

`k=(123)/(10):(41)/(4)=(492)/(410)`

Simplify

`k=(6)/(5)`

Third case

`x=16(3)/(4)=(16*4+3)/(4)=(67)/(4)`

`y=20(1)/(10)=(20*10+1)/(10)=(201)/(10)`

`k=(y)/(x)`

substitute

`k=(201)/(10):(67)/(4)=(804)/(670)`

Simplify

`k=(6)/(5)`