Answer:
B. \(175\text{ ft}^2\)
Step-by-step explanation:
Let x be the unknown side of larger rectangle.
We have been given that corresponding sides of two similar rectangles are 14 ft and 8 ft. The area of the smaller rectangle is \(57ft^2\).
First of all, we will divide area of small rectangle by given side of small rectangle to find the measure of other side of small rectangle as area of rectangle is product of its length and width.
\(\text{Other side of smaller rectangle}=\frac{57\text{ ft}^2}{\text{8 ft}}\)
\(\text{Other side of smaller rectangle}=7.125{ ft}\)
Since both rectangles are similar, so their sides will be in same proportion. We can set an equation as:
\(\frac{x}{7.125}=\frac{14}{8}\)
\(\frac{x}{7.125}=1.75\)
\(\frac{x}{7.125}*7.125=1.75*7.125\)
\(x=12.46875\)
\(\text{Area of larger rectangle}=12.46875\text{ ft}\times 14\text{ ft}\)
\(\text{Area of larger rectangle}=174.5625\text{ ft}^2\)
Upon rounding our answer to nearest whole number we will get,
\(\text{Area of larger rectangle}\approx 175\text{ ft}^2\)
Therefore, the area of larger rectangle is approximately 175 square feet and option B is the correct choice.
