The two triangles are similar, What is the length of DE?

Mathematics

1 answer:

blagie [28]3 years ago

7 0

Answer:

If an angle of one triangle is congruent to the corresponding angle of another triangle and the lengths of the sides including these angles are in proportion, the triangles are similar. The corresponding sides of similar triangles are in proportion.

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What is the solution for x in the given equation? The square root of 9x +7 + the square root of 2x = 7

cestrela7 [59]

Answer:

The solution is x =2 for the given equation $\sqrt{9x+7} +\sqrt{2x}=7$

Step-by-step explanation:

We need to find the solution for x in the given equation.

$\sqrt{9x+7} +\sqrt{2x}=7$

Solving:

Subtract $\sqrt{2x}$ from both sides

$\sqrt{9x+7} =7-\sqrt{2x}$

Taking square on both sides

$(\sqrt{9x+7})^2 =(7-\sqrt{2x})^2\\Using\,\, (a-b)^2 = a^2-2ab-b^2\\9x+7=(7)^2-2(7)(\sqrt{2x})+(\sqrt{2x})^2\\9x+7=49-14\sqrt{2x}+2x\\9x-2x+7-49=-14\sqrt{2x}\\7x-42=-14\sqrt{2x}\\Taking\,\,square\,\,on\,\,both\,\,sides\\(7x-42)^2=(-14\sqrt{2x})^2\\49x^2-2(7x)(42)+(42)^2= 196(2x)\\49x^2-588x+1764=392x\\49x^2-588x+1764-392x=0\\49x^2-980x+1764=0\\Using \,\,quadratic \,\, equation \,\,to \,\, find \,\, value \,\, of \,\, x \\x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\a= 49, \, b= -980 \,\,and\,\, c = 1764$