#1**+3 **

why do you have to enter a more detailed answer if what you post is too short

TaylorSwift Nov 11, 2019

#4**+2 **

Given that the equation through AB has the equation 5y + 2x = 10

Then A has the coordinates (0, 2)

And B has the coordinates (5, 0)

And the slope of the line through AB = [ 2 -0 ] / [ 0 - 5 ] = -2/5

So....the slope of the line through AD is 5/2

So....the equation of the line through AD is

y = (5/2) x + 2

2y - 5x = 4

Since D lies on the x axis, then we have that

2(0) - 5x = 4

x = -4/5

So....the distance AD = sqrt [ (0 - - 4/5)^2 + (2 - 0)^2 ] = sqrt [16/25 + 4] = sqrt [116] / 5

And the distance AB = sqrt [ 5^2 + 2^2 ] = sqrt [ 29]

So.....the area of the rectangle = AD * AB =

sqrt (116 ) sqrt (29) / 5 = sqrt (3364) / 5 = 58/5 units^2 = 11.6 units^2

CPhill Nov 11, 2019