Question

Find the perimeter of rectangle whose length is 24cm and is diagonal is 25 cm.....

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Answer 1

Answer:

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Step-by-step explanation:

Heya,

Given,

Length of rectangle = 24cm

Diagonal = 25cm

Breadth = √(25)² - (24)²

= √49

= 7 cm

So,

Perimeter of rectangle = 2(l + b)

= 2(24 + 7)

= 2×31

= 62cm. ..... Answer

Hope this helps you...:)

Answer 2

Answer:

The Perimeter of the rectangle is 62 cm.

Step-by-step explanation:

Given :

Length of the rectangle = 24 cm

Diagonal of the rectangle = 25 cm

To find :

The perimeter of the rectangle

Solution :

✯$\textsf{\underline{\underline{Breadth of the rectangle - }}}$

Refer the attachment for the diagram.

Solving according to the Pythagoras theorem

Here -

• Hypotenuse = AD = 25 cm
• Base = CD = 24 cm
• Height = AC = y

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

$\tt{\leadsto} \: {(25)^{2} = (24)^{2} + (y)^{2}}\\ \\ \tt{\leadsto} \: 625 = 576 + {y}^{2} \\ \\ \tt{\leadsto} \: {y}^{2} = 625 - 576 \\ \\ \tt{\leadsto} \: {y}^{2} = 49 \\ \\ \tt{\leadsto} \: y = \sqrt{49} \\ \\ \tt{\leadsto} \: y = 7$

Height = 7 cm

$\rule{300}{1.5}$

✯ $\textsf{\underline{\underline{Perimeter of the rectangle -}}}$

$\bigstar\:{\boxed{\tt{Perimeter=2(Length+Breadth)}}}$

• Length = 24 cm
• Breadth = 7 cm

$\tt{\leadsto} \: 2(24 + 7) \\ \\ \tt{\leadsto} \: 48 + 14 \\ \\ \tt{\leadsto} \: 62$

Perimeter = 62 cm

$\therefore$ The Perimeter of the rectangle is 62 cm.