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lianna [129]
3 years ago
14

Shonda is asked to draw a triangle with the following specifications: two angles are complementary two angles have equal measure

the shortest side is half the length of the longest side Which of the following statements about this triangle is true? A. More than one triangle exists with the given conditions, and all instances must be isosceles triangles. B. Exactly one triangle exists with the given conditions, and it must be a right isosceles triangle. C. More than one triangle exists with the given conditions, and all instances must be right triangles. D. No triangle exists with the given conditions.
Mathematics
1 answer:
bogdanovich [222]3 years ago
3 0
"<span>two angles are complementary;" that means the sum of two angles is 90.  Since the sum of all three is 180, the last angle is 90.  It is a right triangle.

"</span><span>two angles have equal measure;" we can't have two angles which are 90, so the other two are equal.  But they sum to 90, so what number plus itself is 90?  45+45=90.  We know now that the triangle has measures 45, 45, and 90.

We know that the legs of the triangle are the same, so we can use the Pythagorean theorem to show that </span>h^2=2l^2, where h is the length of the hypotenuse and l is the length of the legs.

Of course, this means h=l\sqrt2.  But "<span>the shortest side is half the length of the longest side</span>"!  No triangles like this exist.

The only true statement is D
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Step-by-step explanation:

There are several ways you can go at this. Here are 3 of them:

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  2. between the upper left corner and the inside corner at lower right draw a diagonal line to divide the figure into a trapezoid and a triangle.
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The relevant formulas for area are ...

  rectangle: A = LW . . . . . . . . . . . length times width

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  triangle: A = (1/2)bh . . . . . . . . . . . b is the base, h is the height

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Here's what those computations look like:

1. rectangle: 60m wide by 80 m high = 4800 m².

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     area = (1/2)(130 m)(70 m) = 4550 m²

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2. The trapezoid has bases of 80 m and 10 m, and a height of 60 m. Its area is ...

  A = (1/2)(80 m +10 m)(60 m) = 2700 m²

The triangle has a base of 190 m and a height of 80-10 = 70 m. Its area is ...

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3. The bounding rectangle is 190 m by 80 m, so its area is ...

  A = LW = (190 m)(80 m) = 15200 m²

The (negative) trapezoid at right has bases of 10 m and 80 m, and a width of 190-60 = 130 m. Its area is ...

  A = (1/2)(10 m +80 m)(130 m) = 5850 m²

The area of the figure is the difference between these:

  figure area = 15200 m² -5850 m² = 9350 m² . . . figure area

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\huge{\underbrace{\overbrace{\mathfrak{\pink{Answer:}}}}}

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