Question

The dimensions of a garden in the shape of a right triangle are measured in feet (ft). This diagram shows one dimension, in inches (in.), of a scale drawing of the garden and the scale used to create the drawing.

Answer 1

The length of the longest side of the actual garden in feet is 37.5 ft. (Option C).

How to calculate the length of the longest side of the garden?

The length of the longest side of the actual garden is calculated by applying the formula for the area of a triangle as follows;

A = ¹/₂ x b x h

where;

• b is the base of the triangle
• h is the height of the triangle

bh = 2A

h = 2A/b

h = (2 x 54 in² ) / ( 9 in)

h = 12 in

The length of the longest size of the garden in inches is calculated by applying Pythagoras theorem;

c = √ (b² + h²)

c = √ (9² + 12²)

c = 15 in

The length of the longest side of the actual garden in feet is calculated as follows;

scale = 2 in : 5 ft

c = 5 ft / 2in x 15 in

c = 37.5 ft