Question

(ii) Find the diagonal of a square whose side is 10 cm.​

Answer 1

Answer:

• Diagonal is 14.14 cm (approx).

Step-by-step explanation:

Given :-

• Measure of sides of square is 10 cm.

To find :-

• Length of diagonal.

Solution :-

Let, Diagonal of square be AC or x cm.

Square be ABCD.

AB and BC be sides of square.

AB and BC measure will be 10 cm because measure of all sides of square are equal.

We know,

Measure of all angles of square are 90°.

Thus,

∆ABC is a right angle triangle.

By Pythagoras theorem that is:

• Pythagoras theorem is the theorem which states that square of hypotenuse is equal to the sum of squares of the other two sides of right angle triangle.
• Hypotenuse is the longest side of right angle triangle. This side is opposite to 90° angle.
• Formula of Pythagoras theorem is: Hypotenuse² = Base² + Perpendicular²

Now,

Perpendicular = AB = 10 cm.

Base = BC = 10 cm.

Hypotenuse = AC = x

Put all values in Pythagoras theorem :

⇒(x)² = (BC)² + (AB)²

⇒ x² = (10)² + (10)²

⇒ x² = 100 + 100

⇒ x² = 200

⇒x = √200

⇒x = 14.14 (approx)

x is AC which is Hypotenuse of ∆ABC and AC is diagonal of square.

Thus,

Diagonal is 14.14 cm (approx).

Answer 2

${\large{\rm{\underline{Given \; that}}}}$

$\; \; \; \;{\bullet{\leadsto}}$ Side of square = 10 cm.

${\large{\rm{\underline{To \; find}}}}$

$\; \; \; \;{\bullet{\leadsto}}$ Diagonal of square

${\large{\rm{\underline{Solution}}}}$

$\; \; \; \;{\bullet{\leadsto}}$ Diagonal of square = 14.14 cm

${\large{\rm{\underline{Using \: concept}}}}$

$\; \; \; \;{\bullet{\leadsto}}$ Phythagoras theorm formula

${\large{\rm{\underline{Using \: formula}}}}$

$\; \; \; \;{\bullet{\leadsto}}$ AC² = BC² + AB²

${\large{\rm{\underline{Full \; Solution}}}}$

$\; \; \; \; \; \; \;{\bullet{\mapsto}}$ Given square named ABHI.

$\; \; \; \; \; \; \;{\bullet{\mapsto}}$ Let the diagonal be x.

$\; \; \; \; \; \; \;{\bullet{\mapsto}}$ Side of square ABHI is 10 cm and we all know that the side of square is always equal.

$\; \; \; \; \; \; \;{\bullet{\mapsto}}$ And we also know that the measure of all interior angles of square is 90°

$\; \; \; \; \; \; \;{\bullet{\mapsto}}$ Here according to the attachment (1st) ABI form a right angled triangle.

$\; \; \; \; \; \; \;{\bullet{\mapsto}}$ So we have to use phythagoras theorm here.

~ Let's put the values according to the formula of phythagoras theorm.

➨ AC² = BC² + AB²

Here,

AC denotes assumption x'

AB denotes 10 cm

Base denotes 10 cm

➨ x² = 10² + 10²

➨ x² = 100 + 100

➨ x² = 200

➨ x = √200

➨ x = 14.14 cm

${\small{\pink{\frak{Henceforth, \: diagonol \: of \: square \: is \: 14.14 \: cm}}}}$

Phythagoras theorm

It state that in right angled ∆ the square of hypotenuse are equal to the other two sides The sides of this ∆ has been named after perpendicular , Base and Hypotenuse. Here, the hypotenuse is the longest side of the ∆ and it is the opposite side 90°

Diagram is in attachment (2)