Question

Mr. Grimm is trying to build a playground set in his backyard. Part of the playground set will have a slide. The ladder is 5 feet tall, and the slide is 7 feet long. What is the distance between the ladder and the bottom of the slide? Round your answer to the nearest tenth.

Answer 1

Answer:

4.9 ft

Step-by-step explanation:

The Pythagorean Theorem tells us that the sum of the square of each leg in a right triangle is equal to the square of the hypotenuse. It can be written as:

$c^2=a^2+b^2$

Where

• a and b are the 2 legs of the triangle, and
• c is the hypotenuse (side opposite of 90 degree angle)

The picture of the problem is attached.

Now, using pythagorean theorem, we can write (letting the distance from base of ladder to base of slide be $x$):

$(5)^2+(x)^2=(7)^2$

Now solving for $x$:

$(5)^2+(x)^2=(7)^2\\25+x^2=49\\x^2=49-25\\x^2=24\\x=\sqrt{24}=4.9$

Hence, the distance between the ladder and the bottom of the slide is 4.9 ft (rounded to the nearest tenth)