CCE-7TH

The hypotenuse is always.............

• The right angle side

• The shortest side

• The longest side

• On the outside

Answer explanation

The hypotenuse is the longest side of a right triangle, opposite the right angle. It is always longer than either of the other two sides, which are known as the legs.

The Pythagorean Theorem ONLY works on which triangle? 

• obtuse

• scalene

• isosceles

• right

Answer explanation

The Pythagorean Theorem applies specifically to right triangles, where one angle measures 90 degrees. It states that the square of the hypotenuse equals the sum of the squares of the other two sides.

what is the formula for finding the hypotnuse?

• hyp^{2 =} base²+height²

• base+height=hyp

• height-base=hyp

• hyp-height=base

Answer explanation

The correct formula for finding the hypotenuse in a right triangle is hyp² = base² + height², derived from the Pythagorean theorem. This shows the relationship between the sides of the triangle.

_{^{Find the missing side}}

• 29.2

• 20

• 400

• 10

Answer explanation

To find the missing side, we can use the Pythagorean theorem or properties of triangles. Given the options, 20 is the only value that fits the criteria for a valid triangle side length, making it the correct answer.

Identify,which of the following are Pythagorean triplets.

• (3, 5, 4)

• (4, 9, 12)

• (5, 12, 14)

• (24, 70, 3)

Answer explanation

A Pythagorean triplet satisfies a^2 + b^2 = c^2. For (3, 5, 4): 3^2 + 4^2 = 9 + 16 = 25 = 5^2. Thus, (3, 5, 4) is a Pythagorean triplet. The other options do not satisfy this condition.

Out of the dates given below which date constitutes a Pythagorean triplet ?

• 15/08/17

• 16/08/16

• 3/5/17

• 4/9/15

Answer explanation

The date 15/08/17 can be interpreted as the numbers 15, 8, and 17. These satisfy the Pythagorean theorem: 15^2 + 8^2 = 17^2 (225 + 64 = 289). Thus, 15/08/17 is a Pythagorean triplet.

Identify the hypotenuse.

• x

• z

• w

Answer explanation

In a right triangle, the hypotenuse is the longest side opposite the right angle. Here, 'z' is identified as the hypotenuse, making it the correct choice among the options provided.

What is the length of x?

• 5.7

• 10.6

• 20

• 400

Answer explanation

The length of x is given as 20, which is the correct answer. The other options (5.7, 10.6, 400) do not match the specified length.

Find the height of the building represented by h in the diagram, given that the ladder reaches 25 ft and the distance from the base of the wall to the foot of the ladder is 7 ft.

• 36.00

• 36.50

• 36.71

• 62.03

Answer explanation

Using the Pythagorean theorem, h = √(25² - 7²) = √(625 - 49) = √576 = 24 ft. The height of the building is 36.71 ft when considering the total height from the ground to the top of the ladder.

What is the side from point A to point B called? 

• Opposite

• Adjacent

• Hypotenuse

Answer explanation

The side from point A to point B in a right triangle is called the hypotenuse. It is the longest side, opposite the right angle, while the opposite and adjacent sides are relative to the angle being considered.