the length and breadth of a rectangle are (a-5b)units and (7a-b) units respectively. the perimeter of rectangle is equal to perimeter of a square. find how much is the area of rectangle less than that of square
Answers
Answer:
perimeter of rectangle=2(l+b)
2(a+5b+7a-b)
2a+10b+14a-2b
p=16a-8b=the area of square
therefore side of square 16a-8b divided by 4
4a+2b=side of square
area of square =4a+2bX4a+2b
(a+b)2=a2+2ab+b2
so area =16a2+16ab+4b2 (1)
area of rctangle =lXb=(a+5b)X(7a-b)
=7a2-ab+35ab-5b2 (2)
(1)-(2)=9a2-18ab+9b2 this much is the area of rectangle less than that of square
0
9a+b
0
Step-by-step explanation:
perimeter of rectangle=2(l+b)
=2{(a+5b)+(7a-b)}
=2(a+5b+7a-b)
=2a+10b+14a-2b
=16a+8b
perimeter of rectangle=perimeter of sguare
16a+8b = 16a+8b
side of square=16a+8b/4
=4a+2b
area of square=side x side
=4a+2b x 4a+2b
=16a²+16ab+4b²
area of rectangle=l x b
=a+5b x 7a+b
=7a²+34ab-5b²
difference in area=(16a²+16ab+4b²)-(7a²+34ab-5b²)
=9a²-18ab-9b²
HOPE MY ANSWER HELPED YOU!