Question

Find the perimeter of a rectangle whose length is 4 cm greater than its height, and whose area is 60 cm².

Answer 1

32 cm

Explanation:

height = x

length = x+4

x(x+4)=60

x^2 +4x=60

make it into quadratic formula

x^2 + 4x - 60 =0

a=1

b=-4

c=-60

4^2-4*1*(-66)

discriminant equals to 256

square root of 256 equals to 16

x=-4+16/2 = 6

x=-4-16/2 = -10

we will use 6

length is x+4 so 6+4 = 10

width is x = 6

10 plus 10 = 20

6 plus 6= 12

20+12=32 cm

Answer 2

Perimeter of the rectangle = 32 cm

Explanation:

Explanation:-

Let the height of the rectangle = 'x' cm

Thus the length of the rectangle = x + 4 cm

Perimeter of the rectangle = 2 ( length + height )

Area of the rectangle = length X height

Given area of the rectangle = 60 cm²

( length X height ) = 60

( x + 4) x =60

x² + 4 x - 60 =0

x² + 10 x- 6 x - 60 =0

x ( x+10) - 6 ( x + 10 ) =0

(x+10) ( x -6 ) = 0

x = -10 and x =6

we can choose x =6

The height of the rectangle(H) = 'x' = 6 cm

The length of the rectangle (L)= 6 + 4 = 10cm

Perimeter of the rectangle = 2 ( length + height )

= 2 ( 10 + 6 )

= 32 cm

∴ Perimeter of the rectangle = 32 cm