Question

Bill is staking out a location to build a rectangular deck that will be 8 feet wide and 15 feet long. Tyrone has two boards, one that is 8 feet long and one that is 7 feet long. He puts the two boards together, end to end, and lays them on the diagonal of the deck area, where they just fit. What should he tell Bill?

a) The boards will not fit diagonally on the deck.
b) The diagonal of the deck is longer than 15 feet.
c) The diagonal of the deck is shorter than 15 feet.
d) The boards fit perfectly diagonally on the deck.

Answer 1

The two boards will not fit diagonally on the 8x15-foot deck. Option (B) is correct.

Step-by-step explanation:

Geometry is defined as “a branch of mathematics that deals with the measurement, properties, and relationships of points, lines, angles, surfaces, and solids.” Put even more simply, geometry is a type of math that deals with points, lines, shapes, and surfaces.

Geometry is a kind of mathematics that deals with shapes and figures. Geometry explains how to build or draw shapes, measure them, and compare them. People use geometry in many kinds of work, from building houses and bridges to planning space travel.

To determine if the two boards will fit diagonally on the deck, we can use the Pythagorean theorem. The diagonal of a rectangle can be found by calculating the square root of the sum of the squares of the length and width. In this case, the diagonal of the deck would be the square root of (8^2 + 15^2), which is the square root of 289. Simplifying, we find that the diagonal is 17 feet. Since the two boards, when placed end to end, have a total length of 15 feet, they will not fit diagonally on the deck. So, the correct answer to tell Bill is option a) The boards will not fit diagonally on the deck.