Question

19. If x2 – y2 = 7 and x – y = 1, then the length of a diagonal of a rectangle with length and width respectively x cm and y cm will be
(A) 5 cm
(B) 6 cm
(C) 7 cm
(D) 8 cm
(E) None of the above/More than one of the above

Answer 1

Explanation:

If x2 – y2 = 7 and x – y = 1, then the length of a diagonal of a rectangle with length and width respectively x cm and y cm will be

(A) 5 cm

(B) 6 cm

(C) 7 cm✓✓✓✓

(D) 8 cm

(E) None of the above/More than one of the above

Answer 2

Answer:

(A)

Explanation:

$x - y = 1 \: \: \: \: \: \: \: \: ........(i)$

${x}^{2} - {y}^{2} = 7$

$(x + y)(x - y) = 7$

$(x + y)(1) = 7 \: \: \: \: \: \: \: \: (from \: eq.(i))$

$x + y = 7 \: \: \: \: \: \: \: \: ........(ii)$

Adding eq.(i) and (ii),

$2x = 8$

$x = 4$

Putting the value of x in eq.(i),

$4 - y = 1$

$y = 3$

Diagonal of rectangle

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

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

$= \sqrt{ {4}^{2} + {3}^{2} }$

$= \sqrt{16 + 9}$

$= \sqrt{25}$

= 5 cm