Chapter 10.1, Problem 7STP

Joe is cutting three risers for a set of stairs. Each riser is a right triangle with legs $7\frac{1}{2}$ in. and 10 in.

1. What equation could you use to find the length of the third side of a riser?
2. How long will the staircase measure when the 3 risers are installed? Explain.

To determine

To write the equation used to find the third side.

Answer to Problem 7STP

The equation used to find the length of the riser is: ${\left(hypotenuse\right)}^2={\left(base\right)}^2+{\left(height\right)}^2$

Explanation of Solution

Given information:

The given statement is:

“Joe is cutting three risers for a set of stairs. Each riser is a right triangle with legs $7\frac{1}{2}in.$ and $10in$ .

The equation used to find the length of the riser is:

${\left(hypotenuse\right)}^2={\left(base\right)}^2+{\left(height\right)}^2$

To determine

To find the length of the staircase when the $3$ risers are installed.

Answer to Problem 7STP

The length of the riser is $37\frac{1}{2}in$ .

Explanation of Solution

Given information:

The given statement is:

“Joe is cutting three risers for a set of stairs. Each riser is a right triangle with legs $7\frac{1}{2}in.$ and $10in$ .

Formula used:

The following formula is used:

  ${\left(hypotenuse\right)}^2={\left(base\right)}^2+{\left(height\right)}^2$

Calculation :

The solution can be obtained by:

$\begin{array}{l}{\left(hypotenuse\right)}^2={\left(base\right)}^2+{\left(height\right)}^2\\ {\left(hypotenuse\right)}^2={\left(7\frac{1}{2}\right)}^2+{10}^2\\ {\left(hypotenuse\right)}^2={\left(\frac{15}{2}\right)}^2+{10}^2\\ hypotenuse=\sqrt{\frac{225}{4}+100}\\ hypotenuse=\sqrt{\frac{625}{4}}\\ hypotenuse=\frac{25}{2}=12\frac{1}{2}\end{array}$

The length of the riser can be calculated by:

$\begin{array}{l}\frac{25}{2}\times 3\\ =\frac{75}{2}\\ =37\frac{1}{2}\end{array}$

Hence, the length of the riser is $37\frac{1}{2}in$ .