The length of a rectangle is 27 cm less than five times itswidth. Its area is 56

Question

The length of a rectangle is 27 cm less than five times itswidth. Its area is 56 square cm. Find the dimensions ofthe rectangle. The width is_____cm The sum of a number and its square is 2. Find thenumbers. The product of two consecutive room numbers is 272. Findthe room numbers. The room number of the first roomis_______ The length of a rectangle is 27 cm less than five times itswidth. Its area is 56 square cm. Find the dimensions ofthe rectangle. The width is_____cm The sum of a number and its square is 2. Find thenumbers. The product of two consecutive room numbers is 272. Findthe room numbers. The room number of the first roomis_______

Explanation / Answer

let length of rectangle is l and width is b so according to given data l=5b-27 we know area of rectangle is length*width=lb=(5b-27)*b=56 5b2-27b-56 =0 5b2-35b+8b-56=0     usingfactorization 5b(b-7)+8(b-7)=0      taking commonvalue (b-7)(5b+8)=0 b=7 ,b=-8/5 but as width is not negative we will consider b=width=7cm so length =35-27 =8cm     putting value of width B) let the number is x so according to data x+x2=2 x2+x-2=0 x2+2x-x-2=0 x(x+2)-1(x+2)=0 (x+2)(x-1)=0 x= -2,x=1 so the number is 1 or -2 C)let the room number is Z and its conseutive number isZ+1 soZ(Z+1)=272 Z2+Z-272=0 Z2+17Z-16Z-272=0        writing Z =17Z-16Z Z(Z+17)-16(Z+17)=0 (Z+17)(Z-16)=0 Z=-17 ,Z=16 so room number of first room is may be 16 or -17

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