Question

1. 3 marks - 1, 2

farmer browns gate is beginning to sag and he decides to brace it be welding a steel bar across a diagonal. the gate is 4.20m long and 1.25m high.
a. draw a diagram to represent the dimensions given and the length of the brace.
b. how long will the brace need to be? give your answer to 1 decimal place.

Explanation:

Identify the given dimensions

The gate is a rectangle.
Its length is \(4.20\text{ m}\).
Its height is \(1.25\text{ m}\).

Model with a right triangle

The diagonal brace forms a right triangle.
The legs are \(a = 4.20\text{ m}\) and \(b = 1.25\text{ m}\).
The hypotenuse \(c\) is the brace length.

Apply the Pythagorean theorem

Using Pythagorean Theorem:

$$ c^2 = a^2 + b^2 $$

$$ c^2 = 4.20^2 + 1.25^2 $$

Calculate the brace length

Compute the squares and sum:

$$ c^2 = 17.64 + 1.5625 = 19.2025 $$

$$ c = \sqrt{19.2025} = 4.382... $$

Round to one decimal place

Rounding \(4.382...\) to \(1\) decimal place:

$$ c \approx 4.4\text{ m} $$

Answer:

Question 9a

A diagram representing the gate as a rectangle of length \(4.20\text{ m}\) and height \(1.25\text{ m}\), with a diagonal line representing the brace of length \(d\).

Question 9b

\(4.4\text{ m}\)