Question

Given that the points (-7, 6), (3, 6), (3, -6), and (-7, -6) are vertices of a rectangle, how much longer is the length than the width?

Answer 1

Answer:

Therefore,

The Length is longer than Width by 2 units.

$Length=Width+2$

Step-by-step explanation:

Given:

Let the vertices of a Rectangle be  

A ( -7 , 6)

B ( 3 , 6)

C ( 3 , -6)

D ( -7 ,-6)

To Find:

Relation between Length and Width = ?

Solution:

First we will find the Length and Width of Rectangle by Distance Formula ,

$l(AB) = \sqrt{((x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2} )}$

Substituting the values we get

$l(AB) = \sqrt{((3-(-7))^{2}+(6-6)^{2} )}$

$l(AB) = \sqrt{((10)^{2}+(0)^{2} )}\\l(AB)=\sqrt{100}=10\ unit$

Similarly for BC we will have,

$l(BC) = \sqrt{((3-3)^{2}+(-6-6)^{2} )}\\l(BC)=\sqrt{144}=12\ unit$

Now

Length = 12 units.

Width = 10 units.

Therefore,

Let Length be denoted by "L" and Width by "W" then

$Length=Width+2=10+2=12\\\\\therefore L=W+2$

Therefore,

The Length is longer than Width by 2 units.

$Length=Width+2$