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elena-s [515]
3 years ago
9

The diagonal of a square measured 10 cm. Find the length of a side of the square to the nearest tenth.

Mathematics
1 answer:
Naddika [18.5K]3 years ago
6 0

Answer:

  7.1 cm

Step-by-step explanation:

Let s represent the side length of the square. The Pythagorean theorem tells you the relationship to the diagonal length is ...

  (10 cm)² = s² +s² . . . . the sum of the squares of the legs is the square of the hypotenuse

  100 cm² = 2s² . . . . . . simplify

  50 cm² = s² . . . . . . . . divide by 2

  √(50) cm = s ≈ 7.1 cm . . . . . take the square root

The length of a side of the square to the nearest tenth is 7.1 cm.

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Answer:

  • 52°: angles 4, 13, 18
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Step-by-step explanation:

Where a transversal (t or u) crosses parallel lines (m and n), there are four angles formed at each intersection. Corresponding and vertical angles are congruent.

Angles in a linear pair are always supplementary. Of course, the angles interior to a triangle always total 180°. These facts let you find the relationships of all the angles in the figure.

Angle 13 corresponds to the given angle 52°, so has the same measure. Angles 4 and 18 are vertical angles with respect to those, so also have the same measure. Angles 1 and 3, 14 and 17 are supplementary to the ones just named, so all have measure 128°.

In the same way, angles on the other side of the figure can be found from the one marked 44°. Angles 5, 12, and 15 also have that measure; and angles 2, 6, 11, and 16 are supplementary, 136°. Angles 7 and 10 finish the triangle interior so that its sum is 180°. That means they are 180° -52° -44° = 84°. Of course, angles 8 and 9 are the supplement of that value, 96°.

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  • 128°: angles 1, 3, 14, 17
  • 44°: angles 5, 12, 15
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  • 96°: angles 8, 9
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