Q 6.108 - Intermediate Algebra

Question

A meditation garden is in the shape of a right triangle, with one leg $7$ feet. The length of the hypotenuse is one

more than the length of the other leg. Find the lengths of the hypotenuse and the other leg.

Step-by-Step Solution

Answer

The length of the hypotenuse is $25 feet$ and the length of the other leg is $24 feet.$

Step 1. Given Information

There is a meditation garden in the shape of a right triangle where one leg is $7$ feet and the length of the hypotenuse is one more than the length of the other leg.

We have to find the lengths of the hypotenuse and the other leg.

Step 2. Assume the lengths of the hypotenuse and the other leg

Let the length of the other leg be x

So, the length of the hypotenuse will be $x+1.$

Step 3. Summarize into an equation

As we know the meditation garden is in the shape of a right triangle, we can use the Pythagoras theorem.

Pythagoras theorem is

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

Substitute the values in the variables 
$$\begin{gathered} {\left(x\right)}^2+{\left(7\right)}^2={(x+1)}^2 \\ {x}^2+49=x^2+2x+1 \\ 49-1=2x \\ \frac{48}{2}=x \\ 24=x \end{gathered}$$

Step 4. Substitute the value of x in assumed lengths of the hypotenuse and the other leg

So, the length of the other leg will be $24 feet$

and the length of the hypotenuse will be $24+1=25 feet.$ 

Step 5. Verify the lengths of the hypotenuse and the other leg

Let's verify the lengths of the hypotenuse and the other leg of the right triangle by Pythagoras theorem

$$\begin{gathered} 7^2+{24}^2={25}^2 \\ 49+576=625 \\ 625=625 \end{gathered}$$

Thus, the sides of a right triangle are $7, 24 and 25 feet.$