Answer:
The height of rectangle is 5 inches
Step-by-step explanation:
The correct question is
A rectangle is drawn so the width is 7 inches longer than the height. If the rectangle’s diagonal measurement is 13 inches, Find the height
Let
x -----> the width of the rectangle in inches
y ----> the height of the rectangle in inches
d ---> diagonal measurement of the rectangle in inches
we know that
Applying the Pythagorean Theorem
[tex]d^2=x^{2}+y^{2}[/tex]
we have
[tex]d=13\ in[/tex]
so
[tex]13^2=x^{2}+y^{2}[/tex]
[tex]169=x^{2}+y^{2}[/tex] ----> equation A
[tex]x=y+7[/tex] ---> equation B
substitute equation B in equation A
[tex]169=(y+7)^{2}+y^{2}[/tex]
solve for y
[tex]169=y^2+14y+49+y^{2}[/tex]
[tex]2y^2+14y+49-169=0[/tex]
[tex]2y^2+14y-120=0[/tex]
solve the quadratic equation by graphing
using a graphing tool
The solution is y=5
see the attached figure
therefore
The height of rectangle is 5 inches
