Question

The diagram below shows the dimensions of Tessa’s garden.

C) Tessa decided that she liked the shape of her garden but wanted to have 2 times the area. She drew a design for a garden with every dimension multiplied by 2. Explain the error in Tessa’s design.

Answer 1

Tessa's mistake was to have multiplied each dimension by two instead of multiplying by a square root of two.

Explanation:

we know that

If two figures are similar, then the ratio of its areas is equal to the scale factor squared

Let

z -----> the scale factor

x ----> the area of the enlarged garden

y ----> the area of the original garden

`z^(2)=(x)/(y)`

we have that

If Tessa multiplies each dimension by 2, then the scale factor equals 2.

`z=2`

substitute

`2^(2)=(x)/(y)`

`4=(x)/(y)`

`x=4y`

The area of the enlarged garden will be equal 4 times the area of the original garden

so

If Tessa wanted to have twice as much surface, she must multiply each dimension by a square root of 2.

therefore

Tessa's mistake was to have multiplied each dimension by two instead of multiplying by a square root of two.