Question

The length of a diagonal of a rectangle is 17cm and its perimeter is 46cm. Find the length and breadth of rectangle.​

Answer 1

Step-by-step explanation:

Given -

Perimeter = 46 cm

Diagonal = 17 cm

According to Question -

(AB)² + (BC)² = (AC)²

b² + l² = (17)²

l² + b² = 289 ............ (i)

Perimeter = 46 cm

2(l+b) = 46

l+b = 23 ....... (ii)

Squaring both sides

(l+b)² = (23)²

l² + b² + 2lb = 529

Putting value of l² + b² that we calculated above

289 + 2lb = 529

2lb = 529 - 289

2lb = 240

lb = 120

Then,

$l = \frac{120}{b}$

Putting value of

$l \: = \frac{120}{b}$

on equation (ii)

$\frac{120}{b} \: + b \: = 23 \\ \\ \frac{120 \: + {b}^{2} }{b} = 23 \\ \\ 120 \: + {b}^{2} = 23b \\ \\ {b}^{2} - 23b + 120 \\ \\ {b}^{2} - 8b - 15b + 120 \\ \\ b(b - 8) - 15(b - 8) \\ \\ (b - 8)(b - 15) \\ \\ b = 15 \: or \: 8$

Putting the value of b = 15 or 8 on equation (ii)

$l \: + b = 23 \: \\ \\ if \: w e\: put \: b = 18\\ \\ l \: + 18 = 23 \\ \\ l = 23 - 18 \\ \\ l = 5 \\ \\ now \: if \: we \: put \: b = 5 \\ \\ then\\ \\ l \: + b = 23 \\ \\ l + 5 = 23 \\ \\ l = 18$