Question

The square pyramid has a slant height of 17 units and a vertical height of 15 units. What is the length of one side of the pyramid's base?

Answer 1

Answer:

16 units

Step-by-step explanation:

Think of the slant height (s) and vertical height (v) as being 2 sides of a right angle triangle. The slant height is the hypotenuse. The third side is the distance from the centre of the base to the middle of one side of the base. Since the base is a square, this third side is actually half the side length (x) the question is asking us for.

You can relate these using the Pythagorean Theorem:

$s^2=(0.5x)^2+v^2\\s^2=0.25x^2+v^2\\17^2=0.25x^2+15^2\\289=0.25x^2+225\\0.25x^2=64\\x^2=256\\x=16$

Answer 2

Answer:

16 Units is the right answer

Step-by-step explanation:

We can use the Pythagorean Theorem to find the length of the base.

The equation for the Pythagorean Theorem is

a^2 + b^2 = c^2a  

2

+b  

2

=c  

2

a, squared, plus, b, squared, equals, c, squared

Hint #22 / 5

We see that the hypotenuse of the right triangle is 171717. One leg is xxx and the other leg is 151515.

Hint #33 / 5

We have:

\begin{aligned}a^2+b^2&=c^2\\ x^2 +15^2 & = 17^2 \\ x^2 + 225 & = 289 \\ x^2&=64\\ x & = 8 \\ \end{aligned}  

a  

2

+b  

2

 

x  

2

+15  

2

 

x  

2

+225

x  

2

 

x

​  

 

=c  

2

 

=17  

2

 

=289

=64

=8

​  

 

Hint #44 / 5

The leg that forms half the square base is 888. To find the total length of the base we can multiply.

8 \cdot 2 = 168⋅2=168, dot, 2, equals, 16

Hint #55 / 5

The length of one side of the pyramid's base is 161616 units.