131k views
3 votes
What property of squares would you use to solve the problem below?Given square ABCD. If DA = 7x + 1 and CB=4x+ 22, find DC.

User Qwetty
by
6.1k points

1 Answer

2 votes

In the given image, since we need to find the measure of side DC, given DA and CB in algebraic expression form, we are going to use the third property stated:

"in a square, all sides are congruent" because first we want to find "x" by making DA and CB equal:

7x + 1 = 4 x + 22

and once x is found, we need to find the length of any of the square's sides by using either of the given formulas.

Please select the third option.

The value of DC is then found via:

7 x + 1 = 4 x + 22

subtract 4 x from both sides:

7 x - 4 x + 1 = 22

3 x + 1 = 22

subtract 1 from both sides:

3 x = 21

divide both sides by 3:

x = 21 / 3

x = 7

Then the measure of any side of the square is calculated via for example:

4 x + 22 = 4 * 7 + 22 = 28 + 22 = 50

Then DC = 50

User NPS
by
6.2k points