Using the Pythagorean Theorem: Worded problems

Examples with solutions for Using the Pythagorean Theorem: Worded problems

The Egyptians decided to build another pyramid that looks like an isosceles triangle when viewed from the side.

Each side of the pyramid measures 150 m, while the base measures 120 m.

What is the height of the pyramid?

Since the height divides the base into two equal parts, each part will be called X

We begin by calculating X: $120:2=60$

We then are able to calculate the height of the pyramid using the Pythagorean theorem:

$X^2+H^2=150^2$

We insert the corresponding data:

$60^2+h^2=150^2$

Finally we extract the root: $h=\sqrt{150^2-60^2}=\sqrt{22500-3600}=\sqrt{18900}$

$h=30\sqrt{21}$

$30\sqrt{21}$ m

A ladder leans against a wall, meeting the wall at a height of 9 meters. The base of the ladder is 12 meters from the wall. How long is the ladder?

To find the length of the ladder (hypotenuse), use the Pythagorean theorem: $a^2 + b^2 = c^2$ .

Given: $a = 9$ meters, $b = 12$ meters.

Substitute the known values into the equation: $9^2 + 12^2 = c^2$ .

Calculate: $81 + 144 = c^2$ .

Simplify: $225 = c^2$ .

Find $c$ : $c = \sqrt{225}$ .

Therefore, the length of the ladder is $15$ meters.

15 meters

George draws a right triangle on the wall.

Height of the triangle 5m and the width (the second leg) 10m.

For every meter on the perimeter of the triangle, George needs $\frac{1}{3}$ liter of paint.

How many liters of paint does George need?

$5+\frac{5}{3}\sqrt{5}$ liters