Question

the two sides of a rectangular x & x + 1 if the length of the diagonal of a rectangle is 5 then what is the area of the rectangle

Answer 1

Answer:

12 sq unit

Step-by-step explanation:

the diagonal of rectangle is the hypotenuse of triangle

sides are x and x + 1

hypotenuse is 5

${5}^{2} = {x}^{2} + {(x + 1)}^{2} \\ 25 = {x}^{2} + {x}^{2} + 2x + 1 \\ 25 = 2 {x}^{2} + 2x + 1 \\ 2 {x}^{2} + 2x + 1 - 25 = 0 \\ 2 {x}^{2} + 2x - 24 = 0 \\ 2( {x}^{2} + x - 12) = 0 \\ {x}^{2} + x - 12 = 0 \\ {x}^{2} + 4x - 3x - 12 = 0 \\ x(x + 4) - 3(x + 4) = 0 \\ (x + 4)(x - 3) = 0 \\ x + 4 = 0 \: \: \: \: \: x - 3 = 0 \\ x = - 4 \: \: \: \: \: \: \: \: \: x = 3$

we take the positive value of x as length cannot be negative

the sides are

x = 3

x + 1 = 3 + 1 = 4

area of rectangle = l × b

= 4 × 3

= 12 sq unit

hope you get your answer