Question

In the diagram, qudrilaterals FBAG and CDEF are rectangles. How long is DE rounded to the nearest tenth?

Answer 1

The length of segment DE is determined as 7.2.

How to calculate the length of DE?

The length of segment DE is calculated by applying the following formula as shown below;

Since the length CD = 12, FE = 12

FG = 12 - 7

FG = 5

Also, FG = BA = 5

The length CA is calculated by applying Pythagoras theorem as follows;

CA = √ (CB² + BA²)

CA = √ (3² + 5²)

CA = 5.83

The length of AE is calculated using proportion of lengths;

CA/BA = AE / EG

5.83 / 5 = AE / 7

AE = 7 x (5.83 / 5)

AE = 8.16

The total length of CE = 5.83 + 8.16 = 13.99

The length of DE is calculated as follows;

DE = √ (CE² - CD²)

DE = √ (13.99² - 12²)

DE = 7.2

Answer 2

The length of DE is 7.2 units.

Step-by-step explanation:

In the figure:

`\begin{gathered} CD=FG+GE\text{ (Opposite sides of a rectangles)} \\ 12=FG+7 \\ FG=12-7 \\ FG=5 \end{gathered}`

Triangles CBA and AGE are similar, thus:

`\begin{gathered} (CB)/(BA)=(AG)/(GE) \\ (3)/(5)=(AG)/(7) \\ AG*5=3*7 \\ AG=(21)/(5) \\ AG=4.2\text{ units} \end{gathered}`

Thus, we have that:

`\begin{gathered} BF=AG=4.2 \\ DE=CB+BF\text{ (Opposite sides of a rectangle)} \\ DE=3+4.2 \\ DE=7.2\text{ units} \end{gathered}`

The length of DE is 7.2 units.