Respuesta :
We can solve this by using the Pythagorean theorem which is below:
[tex]a^2 + b^2 = c^2[/tex]
Or we can say
[tex]w^2 + h^2 = d^2[/tex]
w = widht
h = height
d = diagonal measure
With that said, we know the height is .75 times the width so .75w. We also know d = 34, which is our diagonal measure.
w = don't know yet but need to find
h = .75w
d = 34
Now lets plugin the information we know into our equation
[tex]w^2 + h^2 = d^2[/tex]
[tex]w^2 + (.75w)^2 = 34^2[/tex]
Now lets to the math
[tex]w^2 + (.75w)^2 = 34^2[/tex]
[tex]w^2 + (.75w)^2 = 1156[/tex]
[tex]w^2 + .5625w^2 = 1156[/tex]
Combine like terms
[tex]w^2 + .5625w^2 = 1156[/tex]
[tex]1.5625w^2 = 1156[/tex]
Divide both sides of the equal sign by 1.5625
[tex]\frac{1.5625w^2}{1.5625} = \frac{1156}{1.5625}[/tex]
[tex]w^2 = 739.84[/tex]
Now take the square root on both sides of the equal sign
[tex]\sqrt{w^2} = \sqrt{739.84}[/tex]
[tex]w = 27.2[/tex]
So the width is 27.2
We can check this by putting 27.2 back into our original equation
[tex]w^2 + (.75w)^2 = 34^2[/tex]
[tex]27.2^2 + (.75\times 27.2)^2 = 34^2[/tex]
[tex]a^2 + b^2 = c^2[/tex]
Or we can say
[tex]w^2 + h^2 = d^2[/tex]
w = widht
h = height
d = diagonal measure
With that said, we know the height is .75 times the width so .75w. We also know d = 34, which is our diagonal measure.
w = don't know yet but need to find
h = .75w
d = 34
Now lets plugin the information we know into our equation
[tex]w^2 + h^2 = d^2[/tex]
[tex]w^2 + (.75w)^2 = 34^2[/tex]
Now lets to the math
[tex]w^2 + (.75w)^2 = 34^2[/tex]
[tex]w^2 + (.75w)^2 = 1156[/tex]
[tex]w^2 + .5625w^2 = 1156[/tex]
Combine like terms
[tex]w^2 + .5625w^2 = 1156[/tex]
[tex]1.5625w^2 = 1156[/tex]
Divide both sides of the equal sign by 1.5625
[tex]\frac{1.5625w^2}{1.5625} = \frac{1156}{1.5625}[/tex]
[tex]w^2 = 739.84[/tex]
Now take the square root on both sides of the equal sign
[tex]\sqrt{w^2} = \sqrt{739.84}[/tex]
[tex]w = 27.2[/tex]
So the width is 27.2
We can check this by putting 27.2 back into our original equation
[tex]w^2 + (.75w)^2 = 34^2[/tex]
[tex]27.2^2 + (.75\times 27.2)^2 = 34^2[/tex]
