Find the area of a rectangle that has a diagnol of 13 cm and a height of 5 cm.
Make a diagram, then notice that you have a right-angled triangle with height=5, hypotenuse=13 and base b
so
b^2 + 5^2 = 13^2
b^2 + 25 = 169
b^2 = 144
b= √144
b = 12
so area = base x height = 12(5) = 60
Thank you !
To find the area of a rectangle, we need the length and width of the rectangle. However, you have provided the diagonal and the height of the rectangle.
To find the length and width, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right-angled 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).
Let's denote the length of the rectangle as "l", the width as "w", and the diagonal as "d".
Using the Pythagorean theorem, we can write the equation as:
l^2 + w^2 = d^2
In this case, the diagonal (d) is given as 13 cm, and the height (w) is given as 5 cm. We need to find the length (l).
Substituting the given values into the equation, we have:
l^2 + 5^2 = 13^2
Expanding and simplifying the equation, we get:
l^2 + 25 = 169
Moving 25 to the other side of the equation, we have:
l^2 = 144
Taking the square root of both sides, we get:
l = √144
l = 12 cm
Now that we have the length and width of the rectangle, we can find the area by multiplying the length and width:
Area = length × width
Area = 12 cm × 5 cm
Area = 60 cm²
Therefore, the area of the rectangle is 60 cm².