DSQ: Calculating whether rectangles are similar

Practice Questions

GMAT Quantitative Reasoning › DSQ: Calculating whether rectangles are similar

Questions

6

1

You are given two rectangles, $\textup{Rect } ABCD$ and $\textup{Rect } EFGH$

True or false: $\textup{Rect } ABCD \sim \textup{Rect } EFGH$ .

Statement 1: $AB \cdot FG= BC \cdot EF$

Statement 2: $AB \cdot GH= CD \cdot EF$

2

You are given two rectangles, $\textup{Rect } ABCD$ and $\textup{Rect } EFGH$ .

Let the perimeter of $\textup{Rect } ABCD$ be , and let the perimeter of $\textup{Rect } EFGH$ be .

Let the area of $\textup{Rect } ABCD$ be and the area $\textup{Rect } EFGH$ be .

True or false: $\textup{Rect } ABCD \sim \textup{Rect } EFGH$ .

Statement 1: $\left (\frac{p }{q} \right ) ^{2}= \frac{r}{s}$

Statement 2: $\frac{AC}{EG} = \frac{p}{q}$

3

Rectangles

Note: Figure NOT drawn to scale.

Refer to the above figure, which shows a rectangle divided into two smaller rectangles.

True or false: $\textup{Rect } ABCF \sim \textup{Rect } CDEF$ .

Statement 1: $CF = \sqrt{AF \cdot FE}$

Statement 2: $AF \cdot FE = AB \cdot DE$

4

You are given two rectangles, $\textup{Rect } ABCD$ and $\textup{Rect } EFGH$

True or false: $\textup{Rect } ABCD \sim \textup{Rect } EFGH$ .

Statement 1: $\frac{AC}{EG} = \frac{BD}{FH}$

Statement 2: $\frac{AB}{EF} = \frac{BC}{FG}$

5

You are given two rectangles, $\textup{Rect } ABCD$ and $\textup{Rect } EFGH$ .

Let the perimeter of $\textup{Rect } ABCD$ be , and let the perimeter of $\textup{Rect } EFGH$ be .

True or false: $\textup{Rect } ABCD \sim \textup{Rect } EFGH$ .

Statement 1: $\frac{AB}{EF} = \frac{p}{q}$

Statement 2: $\frac{AD}{EH} = \frac{p}{q}$

6

You are given two rectangles, $\textup{Rect } ABCD$ and $\textup{Rect } EFGH$ .

Let the perimeter of $\textup{Rect } ABCD$ be , and let the perimeter of $\textup{Rect } EFGH$ be .

Let the area of $\textup{Rect } ABCD$ be and the area $\textup{Rect } EFGH$ be .

True or false: $\textup{Rect } ABCD \sim \textup{Rect } EFGH$ .

Statement 1: $\frac{p^{2}}{q^{2}} = \frac{r}{s}$

Statement 2: $\frac{AB}{EF} = \frac{p}{q}$

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