Question

The diagonal of a rectangle measures 25cm. The width of the rectangle is 7cm. How do you find the length of the rectangle in cm?

Answer 1

The height (length) is `"24 cm"`.

Explanation:

The diagonal of a right triangle is the hypotenuse and is designated as side `c`. The width of a right triangle is side `b`, and the height is side `a`. You are looking for side `a`.

The Pythagorean equation is `c^2=a^2+b^2`.
`c="25 cm"`
`b="7 cm"`
`a=?`

Rearrange the equation to solve for side `a`.

`a^2=c^2-b^2`

Substitute the known values into the equation.

`a^2=(25"cm")^2-(7"cm")^2=`

`a^2=625"cm"^2"-"49"cm"^2=`

`a^2=576"cm"^2`

Take the square root of both sides.

`sqrt(a^2)=sqrt(576"cm"^2")`

`a="24 cm"`