Question

A frame is 5in wider than its height. Its area is 66in2. Find the width and the height of the rectangular picture frame?

representative:

equation:

solution:

answer:

Answer 1

Step-by-step explanation:

let x inches be height

then width =x+5 inches

area =width×height=66in²

x(x+5)=66in²

x²+5X-66=0

-b+/-√289/2=-5+/-17/2=-22/2 or 12/2

-11 or 6

so x=6(11 is not used because negative cannot be a distance)

so hieght=6in

width=11in

Answer 2

Given,

The rectangular frame is 5 inches wider than its height.

The area of the rectangular frame is 66 in²

To find,

The width and height of the rectangular picture frame.

Solution,

We can simply solve this mathematical problem by using the following mathematical process.

Let, the height of the rectangular frame = x inches

So,

Width of the rectangular frame will be = (x+5) inches

Area of the rectangular frame will be = Height × Width = x × (x+5) = (x²+5x) in²

According to the data mentioned in the question,

(x²+5x) = 66

x²+5x-66 = 0

x²+11x-6x-66 = 0

x(x+11)-6(x+11) = 0

(x+11)(x-6) = 0

Either,

(x+11) = 0

x = -11

Or,

(x-6) = 0

x = 6

Now, height of the rectangular frame cannot be negative. So, (-11) will be omitted.

Thus,

Height of the frame = 6 inches

Width of the frame = 6+5 = 11 inches

Hence, height of the rectangular frame is 6 inches and width of the rectangular frame is 11 inches.