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

Answer:

The constant of proportionality is $k=\frac{6}{5}$

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form $k=\frac{y}{x}$ 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

$x=7\frac{1}{2}=\frac{7*2+1}{2}=\frac{15}{2}$

$y=9$

$k=\frac{y}{x}$

substitute

$k=9:\frac{15}{2}=\frac{18}{15}$

Simplify

$k=\frac{6}{5}$

Second case

$x=10\frac{1}{4}=\frac{10*4+1}{4}=\frac{41}{4}$

$y=12\frac{3}{10}=\frac{12*10+3}{10}=\frac{123}{10}$

$k=\frac{y}{x}$

substitute

$k=\frac{123}{10}:\frac{41}{4}=\frac{492}{410}$

Simplify

$k=\frac{6}{5}$

Third case

$x=16\frac{3}{4}=\frac{16*4+3}{4}=\frac{67}{4}$

$y=20\frac{1}{10}=\frac{20*10+1}{10}=\frac{201}{10}$

$k=\frac{y}{x}$

substitute

$k=\frac{201}{10}:\frac{67}{4}=\frac{804}{670}$

Simplify

$k=\frac{6}{5}$