Question

the length of rectangle is greater than twice it's breadth by 2 cm.The length of its diagonal is 13cm.Find the length and breadth of rectangle
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Answer 1

Answer:

length=12cm and breadth=5cm

Step-by-step explanation:

let breadth be xcm

xslength =2x+2

diagonal =13cm

so,

${x}^{2} + ( {2x + 2})^{2} = {13}^{2} \\ {x}^{2} + 4 {x}^{2} + 8x + 4 = 169 \\ 5{x}^{2} + 8x - 165 = 0 \\ 5 {x}^{2} - 25x + 33x - 165 = 0 \\ 5x(x - 5) + 33(x - 5) = 0 \\( 5x + 33)(x - 5) = 0 \\ so \: either(5x + 33 )= 0 \: or(x - 5) = 0$

if (5x+33)=0. if (x-5)=0

or, x=-33/5. or, x=5

as, x can not be negative, x=5

so, 2x+2=2*5+2=12

Answer 2

Answer:

Step-by-step explanation:

Breadth of rectangle be x

Length of rectangle = 2x + 2

Length of diagonal = 13 cm

x^2 + (2x + 2)^2 = 13^2 { Pythagorean theorem)

x^2 + 4x^2 + 8x + 4 = 169

5x^2 + 8x +4 - 169 = 0

5x^2 + 8x - 165 = 0

(5x + 33) (x - 5) =0

measurement cannot be in negative value. so x - 5 =0

x = 5

Breadth of rectangle = 5cm

Length of rectangle  = 12cm