Solve each problem. See Example 5. Height of a Carving of Lincoln Assume that Lincoln was 6 1/3 ft tall and his head was 3/4 ft long. Knowing that the carved head of Lincoln at Mt. Rushmore is 60 ft tall, find how tall his entire body would be if it were carved into the mountain.

Key Concepts

Proportionality

Proportionality is a fundamental concept in mathematics that describes the relationship between two quantities where a change in one quantity results in a corresponding change in another. In this problem, the height of Lincoln's carved head compared to his actual height illustrates how to set up a proportion to find the total height of his body based on the height of the carving.

Ratios

A ratio is a comparison of two quantities that shows the relative size of one quantity to another. In this context, the ratio of Lincoln's actual height to the height of his carved head can be used to determine the height of his entire body when scaled up to the 60 ft tall carving. Understanding how to manipulate ratios is essential for solving the problem.

Scaling

Scaling refers to the process of resizing an object while maintaining its proportions. In this scenario, scaling is used to determine the height of Lincoln's entire body based on the height of the carved head. By applying the same scale factor derived from the ratio of the actual height to the carved height, one can accurately calculate the total height of the carving.