Question

Imogen sees a design for a garden in a magazine. She changes the scale because she wants a smaller garden. The figure below shows both scales and a scale drawing of the yard Magazine scale: 1 inch = 3.5 feet. Imogen's scale: 2 inches = 6 feet. Triangle A B C. Side A is 8 inches, side B is 5 inches, and side C is 10 inches. Which statements about the gardens are true? Select three options. Length A of the magazine’s garden is 28 ft. Length A of Imogen’s garden is 28 ft. Length B of the magazine’s garden is 17.5 ft. Length B of Imogen’s garden is 18 ft. Length C of the magazine’s garden is 35 ft. Length C of Imogen’s garden is 20 ft.

Answer 1

Length A of the magazine garden is 28 feet is true.

Length B of the Magazine garden is 17.5 feet is true.

Length C of the Magazine garden is 35 feet is true.

Explanation:

Please refer the attached figure.

Given:-

Magazine Scale is 1 inch = 3.5 feet.

Imogen's scale is 2 inches = 6 feet,

Therefore Imogen's scale is 1 inch = 3 feet.

In Triangle ABC,

side a = 8 inches, side b= 5 inches, side c= 10 inches.

To find:- The correct 3 options(actual size of sides of triangle ABC).

Solution:-

In triangle ABC,

Let,

AB=side a =8 inches

BC=side b =5 inches

AC=side c= 10 inches

Now, as per the given scale's of Magazine and Imogen's we can find the actual sizes.

Length A as per Magazine scale (1 inch = 3.5 feet) is,

`\therefore Length\ A=8* 3.5` -------------(as per scale)

`\therefore Length A=28\ feet`

and Length A as per Imogen's scale(1 inch =3 feet) is,

AB = side a

`\therefore Length\ A=8* 3` -------------(as per scale)

`\therefore Length A=24\ feet`

Therefore Length A of the magazine garden is 28 feet is true.

Now, Length B as per Magazine scale (1 inch = 3.5 feet) is,

BC = side b

`\therefore Length\ B=5* 3.5`

`\therefore Length B=17.5\ feet`

Length B as per Imogen's scale (1 inch = 3 feet) is,

BC = side b

`\therefore Length\ B=5* 3`

`\therefore Length B=15\ feet`

Therefore Length B of the Magazine garden is 17.5 feet is true.

Now, Length C as per Magazine scale (1 inch = 3.5 feet) is,

AC = side c

`\therefore Length\ C=10* 3.5`

`\therefore Length C=35\ feet`

Length B as per Imogen's scale (1 inch = 3 feet) is,

AC = side c

`\therefore Length\ C=10* 3`

`\therefore Length B=30\ feet`

Therefore Length C of the Magazine garden is 35 feet is true.