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AnaiyaKirksey8
14.04.2020 •
Mathematics
What is the longest possible side length that is an interger of a triangle whose two shorter sides are 15 and 21?
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Ответ:
In the image attached you can find the Unit 7 homework.
We need to findt he missing measures of each figure.
1.Notice that the first figure is a rectangle, which means opposite sides are congruent so,
VY = 19
WX = 19
YX = 31
VW = 31
To find the diagonals we need to use Pythagorean's Theorem, where the diagonals are hypothenuses.
Also,
, beacuse rectangles have congruent diagonals, which intercect equally.
That means,![ZX = \frac{VX}{2} \approx \frac{36.36}{2}\approx 18.18](/tpl/images/0628/2090/c8502.png)
2.Figure number two is also a rectangle.
If GH = 14, that means diagonal GE = 28, because diagonals intersect in equal parts.
Now, GF = 11, because rectangles have opposite sides congruent.
DF = 28, because in a reactangle, diagonals are congruent.
HF = 14, because its half of a diagonal.
To find side DG, we need to use Pythagorean's Theorem, where GE is hypothenuse
![GE ^{2}=11^{2}+DG^{2}\\28^{2}-11^{2}=DG^{2}\\DG=\sqrt{784-121}=\sqrt{663}\\ DG \approx 25.75](/tpl/images/0628/2090/e9689.png)
3.This figure is also a rectangle, which means all four interior angles are right, that is, equal to 90°, which means angle 11 and the 59° angle are complementary, so
Now, angles 11 and 4 are alternate interior angles which are congruent, because a rectangle has opposite congruent and parallel sides.
Which means
, beacuse it's the complement for angle 4.
Now,
, because it's a base angle of a isosceles triangle. Remember that in a rectangle, diagonals are congruent, and they intersect equally, which creates isosceles triangles.
, by complementary angles.
4.
, by supplementary angles.
5.
, by alternate interior angles.
6.The figure is a rectangle, which means its opposite sides are equal, so
Then, we replace this value in the expression of side WZ
Therefore, side WZ is 29 units long.
7.We know that the diagonals of a rectangle are congruent, so
Then,
Therefore, side PR is 73 units long.