Question

in a square the lengths of two adjacent sides are (2a-3) and (a+6). find the value of a . also find the length of the diagonal.​

Answer 1

Answer:

a = 9

15√2

Step-by-step explanation:

in a square the lengths of two adjacent sides are (2a-3) and (a+6). find the value of a . also find the length of the diagonal.​

in a square all sides are equal so adjacent sides are equal

2a - 3 = a + 6

=> a = 9

a + 6 = 9 + 6 = 15

Side of square = 15

Diagonal of a square = Side√2 = 15√2

Answer 2

Answer: a = 9, Diagonal = $\tt{15\sqrt{2} }$ units

Step-by-step explanation:

Lengths of the adjacent sides of a square = 2a - 3, a + 6

We know that all the sides of a square are always equal in length. Thus, by the above information and this property, we may say that the two lengths given to us are equal. This, mathematically, would mean:

2a - 3 = a + 6

$\tt{=> a = 9 \:units}$

Now, the diagonal of a square = $\tt{\sqrt{2} \times side}$

This formula can be proven as:

All the angles of a square are right angles. Therefore, when we join the two opposite vertices (which makes the diagonal), we get a right angled triangle.

By the Pythagoras Theorem in the formed Triangle, we can say that:

$\tt{Side^{2} + Side^{2} = Diagonal^{2}}$

=> $\tt{Diagonal = Side\sqrt{2} }$

The diagonal in this case:

Side = 2a - 3

Side = 18 - 3

Side = 15 units

$\tt{Diagonal = 15\sqrt{2} }$ units