Question

The diagonal of a rectangle is 17 cm long and its perimeter is 46 cm , find the area of rectangle​

Answer 1

Answer:

120 sq.cm

Step-by-step explanation:

let length = x and breadth = y then  

P = 2 (l + b)

2(x+y) = 46         =>   x+y = 23  

x²+y² = 17² = 289  

D2 = l2+b2

now (x+y)² = 23²  

=> x²+y²+2xy= 529  

=> 289+ 2xy = 529

=> xy = 120  

area = xy = 120 sq.cm

Answer 2

Answer:

Given:-

Diagonal=17cm

Perimeter=46cm

Formula used:-

Perimeter of rectangle=2(l+b)

$Diagonal= \sqrt{ {l}^{2} + {b}^{2} }$

Area of rectangle=l×b

Assumption:-

Let length be x

Breath be y

Perimeter=2(x+y)

46cm=2(x+y)

$x+y= \frac{46}{2}$

x+y=23 (1)

$Diagonal= \sqrt{ {x}^{2} + {y}^{2} }$

${17} = \sqrt{ {x}^{2} + {y}^{2} }$

Area=l×b

Squaring both the sides:-

$289 = {x}^{2} + {y}^{2}$

${x}^{2} + {y}^{2} = 289 \: \: (2)$

By(1):-

$( {x + y})^{2} = {23}^{2}$

${x}^{2} + 2xy + {y}^{2} = 529$

From(2):-

289+2xy=529

2xy=529-289

2xy=240

$xy = \frac{240}{2}$

xy=120

But,

As we know l×b is x×y ,in other words xy

Hence,

$Area=120cm^2$