Answer:
7.07 units
Step-by-step explanation:
Use the Pythagorean theorem for the right triangle:
If a = x, b = x, and c = 10, then
Answer: The length of the rectangle is 35 in.
The width of the rectangle is 28 in.
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Explanation:
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The formula for the area, "A", of a rectangle:
Area (A) = length (L) * width (w) ;
that is: " A = L * w " ;
A = 980 in² (given);
ratio of the length to the width is: " 5 : 4 " (given);
→ Find the length (L) and the width (w).
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→ 980 in² = (5x) * (4x) ;
in which: " 980 in² " is the area of the triangle;
" 5x" = the length (L) of the rectangle, for which we shall solve;
" 4x" = the width (w) of the rectangle, for which we shall solve.
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If we find solve for "x" ; we can solve for "5x" and "4x" (the "length" and the "width", respectively); by plugging in the solved value for "x" ;
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→ 980 in² = (5x) * (4x) ;
↔ (5x) * (4x) = 980 in² ;
→ (5x) * (4x) = (5) * (4) * (x) * (x) = 20 * x² = 20x² ;
→ 20x² = 980 ;
Divide each side by "10" ; by canceling out a "0" on each side of the equation:
→ 2x² = 98 ;
Now, divide each side of the equation by "2" ;
→ 2x² / 2 = 98 / 2 ;
to get:
→ x² = 49 ;
Now, take the "positive square root" of each side of the equation; (since a "length or width" cannot be a "negative value") ;
to isolate "x" on one side of the equation; & to solve for "x" ;
→ ⁺√(x²) = √49 ;
to get:
→ x = 7 ;
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Now, we can solve for the "length" and the "width" ;
→ The length is: "5x" ;
5x = 5(7) = " 35 in " ;
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→ The width is: "4x" ;
4x = 4(7) = "28 in."
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Let us check our answer:
→ A = L * w ;
→ 980 in² = ? 35 in. * 28 in. ?? ;
Using a calculator: "35 * 28 = 980" . Yes! ;
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{ Also note: " in * in = in² " ? Yes! } .
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Answer:
B
C
F
D
H
A
G
E
Step-by-step explanation:
Ok. They are trying to reconstruct the smaller looking triangle in the bigger triangle using angle A as the common angle.
The first statement is always the given.
Second they constructed line segment XY into the bigger triangle so that XY is parallel to BC.
Third, from the construction of the parallel lines we can now find corresponding angles that are congruent. This would be the use of F.
Since we have all three angles in triangle AXY and triangle ABC, then the construction of the smaller triangle we made inside the bigger triangle is similar to the bigger triangle. So we have the triangles are similar. You could say E or D here in my opinion. This is choice D.
Fifth the creation of those fractions of sides being equal comes from us knowing the corresponding sides of similar triangles are proportional. This is choice H.
Things looked cut off for the sixth thing so I can't fully read it, but it is possible a substitution has occured.
The seventh thing is a congruence statement which can be proven by a congruence postulate. The only one listed is SAS. So that is G.
The last thing, since the triangle construction is congruent to the smaller triangle then we know the smaller triangle is also similar to the bigger triangle since the bigger one is also similar to the construction we made. I really think E and D is interchangeable. Choice E goes here.
Answer:
7
Step-by-step explanation:
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