Question

The perimeter
of
the
rectangle
Whose length is 60cm and a diagonal is 61cm.
.
a. 120cm
b. 122cm
C. 71cm
d. 142cm​

Answer 1

✬ Perimeter = 142 cm ✬

Step-by-step explanation:

Given:

• Length of rectangle is 60 cm.
• Meaure of diagonal of rectangle is 61 cm.

To Find:

• What is the perimeter of rectangle ?

Solution: Let ABCD be a rectangle where

• AB = 60 cm ( Length )
• AC = 61 cm ( Diagonal )
• ∠ABC = 90° ( Each angle is of 90°)

Now, using Pythagoras Theorem in ∆ABC right angled at B.

• AB = ( Base of ∆ )
• AC = ( Hypotenuse of ∆ )
• BC = ( Perpendicular )

★ Pythagoras Theorem: H² = P² + B² ★

$\implies{\rm }$ AC² = BC² + AB²

$\implies{\rm }$ 61² = BC² + 60²

$\implies{\rm }$ 3721 = BC² + 3600

$\implies{\rm }$ 3721 – 3600 = BC²

$\implies{\rm }$ 121 = BC²

$\implies{\rm }$ √121 = BC

$\implies{\rm }$ 11 cm = BC

So, Meaure of breadth of rectangle is 11 cm. Therefore,

★ Perimeter = 2(Length + Breadth ) ★

➬ 2 (60 + 11)

➬ 2 $\times$ 71

➬ 142 cm

Hence, Perimeter of rectangle is 142 cm. Option D is correct.

Answer 2

Given that ,

Length of rectangle = 60 cm

Diagonal of rectangle = 61 cm

Let , the breadth of rectangle be " B "

By Pythagoras theorem ,

(61)² = (B)² + (60)²

(B)² = (61)² - (60)²

(B)² = 121

B = √121

B = 11

Now , the perimeter of rectangle is given by

$\sf \large \fbox{Perimeter = 2(l + B) }$

Thus ,

Perimeter = 2(60 + 11)

Perimeter = 2(71)

Perimeter = 142 cm

$\therefore \sf \underline{The \: perimeter \: of \: rectangle \: is \: 142 \: cm}$