Properties of squares

If DE = 16x - 3, EF = 9x + 11, and DF = 52, find HG.

The measure of HG is 25.6

For a square, all the sides of the square are equal

Given the following information

First, find the value of x

Since DE is congruent to EF, therefore:  

16x - 3 = 9x + 11

Collect like terms  

16x - 9x = 3 + 11

7x = 14

x = 2

Find the measure of EH:

Since the diagonals of a rhombus are perpendicular, therefore ∆EHF is a right triangle.

Thus, we would use Pythagorean theorem to find EH  

EH² = EF² - HF²

EF = 9x + 11

Plug in the value of x  

EF = 9(2) + 11 = 18 + 11

EF = 29

HF = 52/2 = 26 (diagonals bisect each other)

EH² = 29² - 26² = 165

EH = √165

EH = 12.8 (nearest tenth)

Find the measure of HG:  

HG = 2(EH)  (diagonals bisect each other)

HG = 2(12.8)

HG = 25.6

Hence the measure of HG is 25.6

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*see attachement for diagram

HG = 25.6

Step-by-step explanation:

Given:

DE = 16x - 3

EF = 9x + 11

DF = 52

Required:

HG

SOLUTION:

✔️First, find the value of x

Thus, since DE is congruent to EF, therefore:

16x - 3 = 9x + 11

Collect like terms

16x - 9x = 3 + 11

7x = 14

Divide both sides by 7

x = 2

✔️Find EH:

Since diagonals of a rhombus are perpendicular, therefore ∆EHF is a right triangle.

Thus, we would use pythagorean theorem to find EH

EH² = EF² - HF²

EF = 9x + 11

Plug in the value of x

EF = 9(2) + 11 = 18 + 11

EF = 29

HF = 52/2 = 26 (diagonals bisect each other)

EH² = 29² - 26² = 165

EH = √165

EH = 12.8 (nearest tenth)

✔️Find HG:

HG = 2(EH)  (diagonals bisect each other)

HG = 2(12.8)

HG = 25.6

the 3rd option is right

step-by-step explanation: