Question

the length of the rectangle is greater than twice its breadth by 10 the length of its diagonal is 25 cm find the length and breadth of the rectangle

Answer 1

Answer: length = 24cm , breadth = 7 cm.

Step-by-step explanation:

Let the length be l cm

Breadth be b cm

Given, l = 2b +10

Applying Pythagoras theorem to the triangle formed by length, breadth and diagonal,

25² = l² + b²

625 = (2b+10)² + b²

625 = 4b² + 40b + 100 + b²

625 - 100 = 5b² + 40b

525 = 5b² + 40b

5b² + 40b - 525 = 0

Dividing throughout by 5,

b² + 8b - 105 = 0

b² + 15b - 7b - 105 = 0

b(b + 15) - 7(b + 15) = 0

(b + 15)(b - 7) = 0

So, b = -15 or b = +7

Since breadth cant be negative.

Hence b = 7 cm.

Hence, l = 2b + 10

= 24 cm.

Answer 2

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