Question

1. mr. hamilton is placing a support plank along the diagonal of a gate. the height of the gate is 5 feet, and the diagonal is 1 foot longer than the width of the gate, as shown below. what is the width, in feet, of the gate? 6 24 3 12

Explanation:

Step1: Let the width of the gate be $w$ feet.

The diagonal is $w + 1$ feet and the height is 5 feet.

Step2: Apply the Pythagorean theorem.

In a right - triangle (the gate forms a right - triangle with height, width and diagonal), $a^{2}+b^{2}=c^{2}$, where $a = 5$, $b = w$ and $c=w + 1$. So, $5^{2}+w^{2}=(w + 1)^{2}$.

Step3: Expand the equation.

$25+w^{2}=w^{2}+2w + 1$.

Step4: Simplify the equation.

Subtract $w^{2}$ from both sides: $25=2w + 1$.

Step5: Solve for $w$.

Subtract 1 from both sides: $24 = 2w$. Then divide both sides by 2, $w = 12$.

Answer:

12