Question

Find the width of the rectangle if its length is 20cmand the length of its diagonal is
25 cm?​

Answer 1

Answer:

The width of the rectangle is 15 cm.

Step-by-step explanation:

Given :

Length of the rectangle = 20 cm

Diagonal = 25 cm

To find :

The Length is the rectangle

Solution :

Solving according to Pythagoras theorem -

In ∆ ACD -

• Hypotenuse = 25 cm
• Base = 20 cm
• Height = x

$\bigstar \: {\boxed{\sf{(Hypotenuse)^{2} = (Base)^{2} + (Height)^{2}}}}$

$\sf{\implies} \: {25}^{2} = {20}^{2} + {x}^{2} \\ \\ \sf{\implies} \: 625 = 400 + {x}^{2} \\ \\ \sf{\implies} \: {x}^{2} = 625 - 400 \\ \\ \sf{\implies} \: {x}^{2} = 225 \\ \\ \sf{\implies} \: x = \sqrt{225} \\ \\ \sf{\implies} \: x = 15$

Height = 15 cm

$\therefore$ The width of the rectangle is 15 cm.

Answer 2

Answer:

15

Let ABCD a rectangle with AD as it's diagonal.

Let ABD a right angled triangle.

So,

AB=20cm

BD=x cm

AD=25 cm

From Pythogoras Theorem we have:

AD²= AB²+BD²

25²= 20²+x²

x²= (25+20)×(25-20)

=45×5

=√225

=15

So, BD=15 cm

Therefore, width of the rectangle is 15 cm

Hope it helps.....!!!!!!