Question

what is the value of x? round your answer to the nearest hundredth. * 10 points barrett is looking at a building on the school grounds which is shaped like a rectangle as shown. he knows the building has a height of 25x feet and a width of 28x feet with a diagonal of 180 feet. 3.6 3.2 4.8 2.4 4.4 5.4 5.2 1.2

Explanation:

Step1: Apply Pythagorean theorem

$$(25x)^2 + (28x)^2 = 180^2$$

Step2: Expand and combine terms

$$625x^2 + 784x^2 = 32400$$
$$1409x^2 = 32400$$

Step3: Isolate $x^2$

$$x^2 = \frac{32400}{1409}$$

Step4: Solve for $x$ and round

$$x = \sqrt{\frac{32400}{1409}} \approx \sqrt{23.00} \approx 4.80$$

Answer:

4.8