Question

• 20 points what is the width and height of the building? round your answer to the nearest hundredth. 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. 48 36 134.4 24 131.2 95.4 155.2 120 126.8 1c height width

Explanation:

Step1: Apply Pythagorean theorem

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

Step2: Expand and simplify terms

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

Step3: Solve for $x^2$ then $x$

$$x^2 = \frac{32400}{1409}$$
$$x = \sqrt{\frac{32400}{1409}} \approx 4.80$$

Step4: Calculate height ($25x$)

$$25 \times 4.80 = 120.00$$

Step5: Calculate width ($28x$)

$$28 \times 4.80 = 134.40$$

Answer:

Height: 120
Width: 134.4