A rectangular picture frame measures 8cm by 4cm.

Question

A rectangular picture frame measures 8cm by 4cm. You want to triple the frames area by adding the same distance x to the length and the width. Write and solve an equation to find the value of x.what are the new dimensions of the picture frame?

Answer 1

Let x = distance added to length and width

 

Original area = 8 * 4 = 32 square cm

 

New area = 96 = (8 + x) * (4 + x)

 

32 + 12x + x² = 96

 

x² + 12x - 64 = 0

 

add 100 to both sides to square it up

x² + 12x - 64 + 100 = 100

x² + 12x + 36 = 100

 

take the square root of both sides

(x + 6)² = 100

 

 

x + 6 = 10

 

x = 4

 

Add 4 cm to both length and width to get dimensions of

 

12 cm for length and 8 cm for width gives an area of 96 square cm