Question

a rectangle has sides of x+3 cm and x -4 cm. what value of x gives an area of 78cmcm

Answer 1

Given area of rectangle = 78 cm sq
Length=x+3
Breath= x-4
According to the question-
Length × breath = area
( x+3)×(x-4)=78
×2 -4x+3x-12=78
x2-x-90=0
x2-10x+9x-90=0
x (x-10)+9 (x-10)=0
(x-10)(x+9)=0
Therefore x=10 or x= -9

Answer 2

Let dimensions of the rectangle are
Leangth = l = (x+3) cm
Breadth=b=(x-4) cm
Area =78 sq cm
lb=78
(x+3)(x-4)=78
x^2-4x+3x-12-78=0
x^2-x-90=0
x^2-10x+9x-90=0
x(x-10)+9(x-10)=0
(x-10)(x+9)=0
x-10=0 or x+9=0
x=10 or x=-9
xshold not be negative
We take x=10
Therefore
Length =l=x+3=10+3=13cm
b=x-4=10-4=6 cm