Question

the diagram shows the placement of a ladder against cheris house. the ladder needs to lean against the house at a height of 24 feet. how far should cheri place the base of the ladder from her house? 1 foot 7 feet 35 feet 49 feet

Explanation:

Step1: Recognize right - triangle situation

The ladder, the house, and the ground form a right - triangle. The height on the house where the ladder leans (vertical side) is $a = 24$ feet, and the distance from the base of the ladder to the house is $b$ (unknown), and assume the length of the ladder is the hypotenuse $c$. If we assume the ladder is a standard 25 - foot ladder (since no length of ladder is given but a common ladder length is used for such problems, and we can also solve in general terms using the Pythagorean theorem $a^{2}+b^{2}=c^{2}$). Here, $a = 24$ and $c = 25$.

Step2: Apply Pythagorean theorem

$b^{2}=c^{2}-a^{2}$. Substitute $a = 24$ and $c = 25$ into the formula: $b^{2}=25^{2}-24^{2}=(25 + 24)(25 - 24)$ (using the difference - of - squares formula $x^{2}-y^{2}=(x + y)(x - y)$). Then $b^{2}=(49)(1)=49$.

Step3: Solve for $b$

Take the square root of both sides. Since $b$ represents a distance, we take the positive square root. So $b=\sqrt{49}=7$.

Answer:

B. 7 feet