Question

7

Jackson is creating a rectangular board game that includes a diagonal line from two of the corners of the game. How long is the diagonal if the board game is 10 inches

long by 8 inches wide? Explain your reasoning. Round your answer to the nearest tenth of an inch.

Helppp

Answer 1

diagonal = = 12.8 inches (to the nearest tenth of an inch)

Explanation:

As shown in the diagram attached to this solution:

Let the Length of the rectangular board = a

Let the width = b

Let the diagonal = d

where:

a = 10 inches

b = 8 inches

d = ?

Triangle ABC in the diagram is a right-angled triangle, therefore, applying Pythagoras theorem:

(hypotenuse)² = (Adjacent)² + (Opposite)²

d² = 10² + 8²

d² = 100 + 64

d² = 164

∴ d = √(164)

d = 12.806 inches

d = 12.8 inches (to the nearest tenth of an inch)

N:B Rounding off to the nearest tenth of an inch is the same as rounding off to 1 decimal place.