Question

In the figure, ABCD and DEFG are squares.AC:FD=7:5, find CE

Answer 1

Given:

The ratio of the diagonals of the squares ABCD and DEFG is:

`AC:FD=7:5`

Required-the value of CE.

Step-by-step explanation:

Given that the ratio of the diagonals of the squares ABCD and DEFG is:

`AC:FD=7:5`

So, the sides will be in the same ratio.

`AD:GD=7:5`

Let the sides of the two triangles ABCD and DEFG be 7x and 5x.

Given that

`AG=3cm`

So, we can write AG as:

`\begin{gathered} AG=AD-GD \\ 3=7x-5x \\ \\ 2x=3....(1) \end{gathered}`

Now, we have to find CE, so we can write CE as:

`\begin{gathered} CE=CD+DE \\ \\ CE=7x+5x \\ \\ CE=12x \\ \\ CE=6(2x) \\ \\ CE=6*3 \\ \\ CE=18cm \end{gathered}`

Final answer: The value of CE is 18 cm.