Question

1. एक आयत की लम्बाई, चौड़ाई से 10 मी अधिक है तथा उसका
क्षेत्रफल 200 वर्ग मी है, तो आयत की लम्बाई तथा चौड़ाई
ज्ञात कीजिए।
(1) 20 मी, 10 मी
(2) 15 मी, 25 मी
(3) 10 मी, 15 मी
(4)25 मी, 30 मी​

Answer 1

Answer:

Breadth of rectangle =  10 m

Length  of rectangle = 20 m

Step-by-step explanation:

Let,

Breadth of rectangle = x

Length  of rectangle = x  + 10

Area of rectangle = 200 m²

Area of rectangle =  length × breadth

⇒ x (x + 10) = 200

⇒ x² + 10x - 200 = 0

⇒ x² + 20x - 10x - 200 = 0

⇒ x (x + 20) - 10 (x + 20) = 0

⇒  (x + 20) ( x - 10) = 0

⇒   (x + 20) or  ( x - 10)

⇒ x + 20   or  x - 10

As side can't be negative it is positive

So,

⇒  x  =  10

Breadth of rectangle =  10 m

Length  of rectangle = x  + 10

⇒ 10 + 10

⇒ 20

Length  of rectangle = 20 m

Answer 2

Given ,

• The length of rectangle is 10 more than its breadth

• Area of rectangle = 200 m²

Let ,

The breadth of rectangle be " x "

Then , length = " x + 10 "

We know that , the area of rectangle is given by

$\boxed{ \sf{Area = l × b }}$

Thus ,

200 = x(x + 10)

200 = (x)² + 10x

(x)² + 10x - 200 = 0

By middle term splitting method ,

(x)² + 20x - 10x - 200 = 0

x(x + 20) - 10(x + 20) = 0

(x - 10)(x + 20) = 0

x = 10 or x = -20

Since , the length can't be negative

Therefore ,

• Breadth of rectangle = 10 m
• Length of rectangle = 20 m