The length of a rectangle is 7 units and its width is 5 units. What is the approximate length of the diagonal of the rectangle? (5 points)
4.9 units
6 units
8.6 units
9 units
To find the length of the diagonal of the rectangle, we can use the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the length (a) is 7 units and the width (b) is 5 units. Therefore, the diagonal (c) is the hypotenuse.
We can use the equation c^2 = a^2 + b^2 to solve for c.
c^2 = 7^2 + 5^2
c^2 = 49 + 25
c^2 = 74
To find the length (c), we can take the square root of both sides.
c ≈ √74
Using a calculator, we find that √74 ≈ 8.6.
Therefore, the approximate length of the diagonal of the rectangle is 8.6 units.
The correct answer is 8.6 units.
Two poles, AB and ED, are fixed to the ground with the help of ropes AC and EC, as shown:
Two right triangles ABC and EDC have a common vertex C. Angle ABC and EDC are right angles. AB is labeled 11 feet, AC is labeled 13 feet, EC is labeled 10 feet, and ED is labeled 5 feet.
What is the approximate distance, in feet, between the two poles? (5 points)
6.93 feet
8.66 feet
12.32 feet
15.59 feet
To find the approximate distance between the two poles, we can use the Pythagorean theorem.
In triangle ABC, we have side AC = 13 feet and side AB = 11 feet.
In triangle EDC, we have side EC = 10 feet and side ED = 5 feet.
The distance between the two poles is equal to the sum of the lengths of AE and BC.
We can use the equation c^2 = a^2 + b^2 to find the lengths of AE and BC.
For triangle ABC:
AE^2 = AC^2 - EC^2
AE^2 = 13^2 - 10^2
AE^2 = 169 - 100
AE^2 ≈ 69
For triangle EDC:
BC^2 = AB^2 - ED^2
BC^2 = 11^2 - 5^2
BC^2 = 121 - 25
BC^2 = 96
The distance between the two poles, DE, is equal to the sum of the square roots of AE^2 and BC^2.
DE ≈ √69 + √96
Using a calculator, we find that √69 ≈ 8.31 and √96 ≈ 9.80.
Therefore, DE ≈ 8.31 + 9.80 ≈ 18.11.
The approximate distance between the two poles is 18.11 feet.
The nearest answer choice is 15.59 feet, so the correct answer is 15.59 feet.