Question

One of the altitudes of the parallelogram shown is units. What is the length of the other altitude? REPLY ASAP PLS

Answer 1

The answer is B or 6 units

Answer 2

Answer:

B. 6 units.

Step-by-step explanation:

We have been given an image of a parallelogram and the length of one altitude of our given parallelogram is $\sqrt{22.5}$ and we are asked to find the length of other altitude of our given parallelogram.

We will use area of parallelogram formula to find the length of other altitude of our given parallelogram.

$\text{Area of parallelogram}=\text{Base length*Height}$, where height represents altitude.

Let us find both bases of parallelogram using distance formula.

$\text{Distance}=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

$\text{Length of vertical base}=\sqrt{(4-1)^2+(8-4)^2}$

$\text{Length of vertical base}=\sqrt{(3)^2+(4)^2}$

$\text{Length of vertical base}=\sqrt{9+16}$

$\text{Length of vertical base}=\sqrt{25}=5$

$\text{Length of horizontal base}=\sqrt{(7-1)^2+(2-4)^2}$

$\text{Length of horizontal base}=\sqrt{(6)^2+(-2)^2}$

$\text{Length of horizontal base}=\sqrt{36+4}$

$\text{Length of horizontal base}=\sqrt{40}$

We can set an equation to find the other altitude of our parallelogram as:

$\text{Altiude}_1*\text{Vertical base}=\text{Altiude}_2*\text{Horizontal base}$

Upon substituting our given values in above equation we will get,

$\sqrt{22.5}*\sqrt{40}=\text{Altiude}_2*5$

$30=\text{Altiude}_2*5$

Let us divide both sides of our equation by 5.

$\frac{30}{5}=\frac{\text{Altiude}_2*5}{5}$

$6=\text{Altiude}_2$

Therefore, the length of the other altitude of our given parallelogram will be 6 units and option B is the correct choice.