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.

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

Step-by-step 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

we have that

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

substitute

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.

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