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?

Question

Eva Abramson · Accepted Answer

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

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"#

Avery Alexander · Answer

undefined To find the length of the rectangle, you can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the diagonal) is equal to the sum of the squares of the other two sides (the length and width of the rectangle).

In this case, the diagonal is 25cm and the width is 7cm. Let's denote the length of the rectangle as 'l'.

Using the Pythagorean theorem, we can set up the equation:

25^2 = l^2 + 7^2

Simplifying this equation, we have:

625 = l^2 + 49

Subtracting 49 from both sides, we get:

576 = l^2

Taking the square root of both sides, we find:

l = √576

Simplifying the square root, we have:

l = 24

Therefore, the length of the rectangle is 24cm.