Question

If the area of a rectangle is 1260 cm2 and its perimeter 146 cm, What is the length of diagonal? ​

Answer 1

Answer:

D =18.385

Step-by-step explanation:

Area of Rectangle = l×b

1260 = l × b --------- 1

perimeter of Rectangle =2(l+b)

146 = 2(l+b). --------- 2

From 1

l = 1260/b --------- 3

From 2

l =146-2b/2. ------- 4

from 3and 4

we get,

b =17.5

by substituting b =17.5 in 2

146 = 2(l+17.5)

l = 55.5

diagonal of Rectangle =√l^2+b^2

D = √55.5^2+17.5^2

= √3080.25+306.25

= 18.385

Therefore,

Diagonal = 18.385

Answer 2

The length of diagonal is 53 cm.

Given - Area and perimeter

Find - Length of diagonal

Solution - Let the length and breadth of rectangle be l and b respectively.

Area of rectangle = length*breadth

1260 = l*b

$l = \frac{1260}{b}$

Perimeter = 2(l+b)

$146 = 2( \frac{1260}{b} + b)$

$73 = \frac{1260}{b} + b$

$73b = 1260 + {b}^{2}$

b² - 73b + 1260 = 0

On solving, we get value of b = 45 and 28.

Length = area/breadth

Length = $\frac{1260}{45} and \: \frac{1260}{28}$

Length = 28 and 45

Diagonal = ✓l² + b²

Diagonal = ✓(28² + 45²)

Diagonal = ✓784 + 2025

Diagonal = ✓2809

Diagonal = 53 cm

Length of diagonal is 53 cm.

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