Question

A rectangle is drawn so the width is 7 inches longer than the height. If the rectangle’s diagonal measurement is 13 inches, don’t the height.

Answer 1

The height of rectangle is 5 inches

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

`d^2=x^(2)+y^(2)`

we have

`d=13\ in`

so

`13^2=x^(2)+y^(2)`

`169=x^(2)+y^(2)` ----> equation A

`x=y+7` ---> equation B

substitute equation B in equation A

`169=(y+7)^(2)+y^(2)`

solve for y

`169=y^2+14y+49+y^(2)`

`2y^2+14y+49-169=0`

`2y^2+14y-120=0`

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