Question

The perimeter of a square field is (4x+8) Find the length of its diagonal. (a) (x + 673 (b) (x + 4) 2 (x + 2)2 (d) (x + 5173​

Answer 1

Answer:

Step-by-step explanation:

if perimeter = 4x+8

so 4a= 4x+8

a= x+2 where a is the side

hence diagonal of the square with side x+2 will be

(x+2) root2

Answer 2

Given

• Perimeter of a square field is (4x+8).

To Find

• Length of its diagonal

Using Formula

$\begin{gathered} {\underline{\boxed{ \rm {\purple{Diagonal \: \: of \: \: square \: = \: \sqrt{2 \: a} }}}}}\end{gathered}$

$\begin{gathered} {\underline{\boxed{ \rm {\blue{Perimeter = 4a }}}}}\end{gathered}$

Solution

If square has a side a , we know that

• Perimeter = 4a

$\bf \longrightarrow \: \: (4x+8) \: = \: 4a$

$\bf \longrightarrow \: \: \frac{(4x+8)}{4} \: = \: a$

$\bf \longrightarrow \: \: \frac{( \cancel4x+ \cancel8 \: ^{2} )}{ \cancel4} \: = \: a$

$\bf \longrightarrow \: \: a \: = \: (x + 2)$

Therefore , the side of square field is (x+2).

Now , we have to find length of the diagonal.

$\begin{gathered} {\underline{\boxed{ \rm {\red{Diagonal \: \: of \: \: square \: = \: \sqrt{2 \: a} }}}}}\end{gathered}$

Substuting the values

$\bf \longrightarrow \: \: Diagonal \: \: of \: \: square \: = \: \sqrt{2 \: (x + 2)}$