Apicture is 4.25 inches wide and 7.75 inches tall. it is mounted in a frame with a border of x inches wide on all sides. if the area of the shaded border is 45 inches squared, what is its width x?

ANSWER:  

Width of border is 1.5 inches            

SOLUTION:

Given,  

Width of the photo graph = 4.25 inches

Height of the photo graph = 7.75 inches  

And it is mounted in a frame with border of x inches, so the dimensions after mounting will be

Width after mounting = (4.25 + x + x) [ since, two sides of photograph will have borders

Height after mounting = (7.75 + x + x) [ since, two sides of photograph will have borders  

Area of border = 45 square inches

As we all know that, photograph will be in rectangular shape,  

Area of photograph =

Area of photograph after mounting =

Now, area of border = Area of photograph after mounting - Area of photograph before mounting

  [by dividing the equation with 4]

As length can’t be negative, x =

Hence , the width x is 1.5 inches

18 units²

step-by-step explanation:

first let's find altitude bd using the distance formula

d = √((y₂ - y₁)² + (x₂ - x₁)²)

bd = √((0 - -3)² + (0 - 3)²)

bd = √18

given the placement of points a and c, we can denote that point d bisects segment ac.

we will call ac the base.

using the distance formula

ac = √((0 - 6)² + (-6 - 0)²)

ac = √72

knowing our base and our height, we can plug these into our triangle area formula

area = (b * h)/2

area = (√18 * √72) / 2

area = (√1296) / 2

area = 36 / 2

area = 18 units²