इफ द लेंथ ऑफ ए रैक्टेंगल इज डिक्रीड बाय 3 यूनिट एंड ब्रेथ इनकरेज्ड बाय फॉर यूनिटी इन द एरिया विद इंक्रीज इन 9 स्क्वायर यूनिट्स अरे प्रेजेंट सिचुएशन एंड लीनियर इक्वेशन इन टू वेरिएबल
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Let the length and breadth of the rectangle be x and y units respectively. Then,
Area =xy sq. units.
If length is reduced by 5 units and the breadth is increases by 3 units, then area is reduced by 9 square units.
∴xy−9=(x−5)(y+3)
⇒xy−9=xy+3x−5y−15
⇒3x−5y−6=0 ...(i)
When length is increased by 3 units and breadth by 2 units, the area is increased by 67 sq. units.
∴xy+67=(x+3)(y+2)
⇒xy+67=xy+2x+3y+6
⇒2x+3y−61=0 ...(ii)
Thus, we get the following system of linear equations:
3x−5y−6=0
2x+3y−61=0
By using cross-multiplication, we have
305+18
x
=
−183+12
−y
=
9+10
1
⇒x=
19
323
=17 and y=
19
171
=19
Hence, the length and breadth of the rectangle are 17 units and 19 units respectively
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