Math  /  Geometry

QuestionRectangle ABCDA B C D is similar to rectangle EBGF.
What is the value of bb in centimters? 45 cm 20 cm 3.2 cm 36 cm

Studdy Solution

STEP 1

What is this asking? We need to find the width of a larger rectangle, knowing it's similar to a smaller rectangle with given dimensions. Watch out! Similar rectangles have proportional sides, not equal sides!

STEP 2

1. Set up the proportion
2. Solve for bb

STEP 3

Alright, awesome students, let's do this!
We've got two similar rectangles, which means their corresponding sides have the *same ratio*.
The smaller rectangle, EBGF, has a height of 44 cm and a width of 99 cm.
The larger rectangle, ABCD, has a height of 1616 cm and a width of bb cm, which is what we're trying to find.

STEP 4

Since the rectangles are similar, the ratio of their heights must equal the ratio of their widths.
Let's write that down: height of ABCDheight of EBGF=width of ABCDwidth of EBGF \frac{\text{height of ABCD}}{\text{height of EBGF}} = \frac{\text{width of ABCD}}{\text{width of EBGF}}

STEP 5

Now, let's **plug in** the values we know: 164=b9 \frac{16}{4} = \frac{b}{9} Look at that beautiful proportion!

STEP 6

To **isolate** our mysterious bb, we'll **multiply** both sides of the equation by 99.
Remember, what we do to one side, we *must* do to the other to keep things balanced.
It's like a seesaw! 9164=9b9 9 \cdot \frac{16}{4} = 9 \cdot \frac{b}{9}

STEP 7

On the right side, the 99s **divide to one**, leaving us with just bb.
Perfect! 9164=b 9 \cdot \frac{16}{4} = b

STEP 8

Now, let's **simplify** the left side.
We can divide 44 into itself to get 11, and divide 44 into 1616 to get 44. 941=b 9 \cdot \frac{4}{1} = b

STEP 9

Which gives us: 94=b 9 \cdot 4 = b

STEP 10

And finally, we **multiply** 99 and 44 to get our **final result**: 36=b 36 = b So, b=36b = 36 cm!

STEP 11

The width, bb, of rectangle ABCD is **36 cm**.

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