Question

a 15 - foot tall tree is next to a slide. the tree is casting a shadow of 22.5 feet and the slide is casting a shadow that is 10.5 feet. how tall is the slide? f 7 ft g 15 ft h 25 ft j 33 ft

Explanation:

Step1: Set up the proportion

Since the tree and the slide form similar right - angled triangles (due to the sun's rays creating similar shadow - height relationships), we can set up the proportion \(\frac{\text{height of tree}}{\text{shadow of tree}}=\frac{\text{height of slide}}{\text{shadow of slide}}\). Let \(h\) be the height of the slide. So, \(\frac{15}{22.5}=\frac{h}{10.5}\).

Step2: Cross - multiply

Cross - multiplying gives us \(22.5h = 15\times10.5\). First, calculate \(15\times10.5=157.5\). So the equation becomes \(22.5h = 157.5\).

Step3: Solve for \(h\)

Divide both sides of the equation \(22.5h = 157.5\) by \(22.5\). \(h=\frac{157.5}{22.5}\). \(157.5\div22.5 = 7\).

Answer:

F. \(7\) ft