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Studentka2010 [4]
3 years ago
6

DEFG is a rectangle. DF = 5x - 3and EG = x + 5. Find the value of x and the length of each diagonal.

Mathematics
2 answers:
erica [24]3 years ago
8 0
d. x = 2, DF = 7, EG = 7
 
DF is equivalent to EG; Therefore, the equation would be like this:

5x - 3 = x + 5
Transfer 3 and x to their opposite side and change their signs.

5x - x = 5 + 3
4x = 8
Find x. Divide both sides by 4.

4x / 4 = 8 / 4
x = 2

Subsitute x in the equation to find the length of each diagonal.

DF = 5x - 3 = 5(2) - 3 = 10 - 3 = 7 ; DF = 7
EG = x + 5 = 2 + 5 = 7 ; EG = 7

Elden [556K]3 years ago
8 0
Answer: d. x = 2, DF = 7, EG = 7
Solution:
by ratio:  DF : EG
                5x - 3 = x + 5
Solving for x:
               
5x -x = 5 + 3
                 x = 2
Substituting x=2 in the expression
               DF = 5x -3 = 5(2) - 3 = 7
               EG = x + 5 = 2 + 5 = 7
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Answer:

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Step-by-step explanation:

In a triangle, the length of two sides added together must exceed the length of the 3rd side. So, since EF is the shortest of the two givens, we know that EF + DF must be greater than DE. So we can plug in these numbers to find the minimum.

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