The longer side of a rectangle is 3cm longer than it’s shorter side if the diagonal is 15cm. What is the area of the rectangle?
Waiting
Pls help me i need the solution
geez -- impatient much?
If the shorter side is x, then
x^2 + (x+3)^2 = 15^2
so now just solve for x.
Or, you might recognize this triangle as a 3-4-5 right triangle, scaled up by a factor of 3.
To find the area of the rectangle, we need to know the lengths of the shorter and longer sides. Let's denote the shorter side as 'x' cm.
According to the given information, the longer side is 3 cm longer than the shorter side, which means the longer side is (x + 3) cm.
Now, we can use the Pythagorean theorem to relate the sides of the rectangle and the diagonal.
The Pythagorean theorem states that, in a right-angled triangle, the square of the hypotenuse (diagonal in our case) is equal to the sum of the squares of the other two sides.
In our scenario, the shorter side, longer side, and diagonal form a right-angled triangle. So, applying the Pythagorean theorem:
(diagonal)^2 = (shorter side)^2 + (longer side)^2
(15 cm)^2 = x^2 + (x + 3)^2
225 cm^2 = x^2 + (x^2 + 6x + 9)
225 cm^2 = 2x^2 + 6x + 9
Now, we have a quadratic equation. We need to solve this equation to find the value of 'x', which represents the shorter side of the rectangle.
By rearranging and solving, we get:
2x^2 + 6x - 216 = 0
Or, x^2 + 3x - 108 = 0
Factoring or using the quadratic formula, we find that x = 9 or x = -12 (we ignore the negative value since length cannot be negative in this context).
The shorter side, x, is 9 cm.
Therefore, the longer side is (x + 3) = 12 cm.
Finally, we can find the area of the rectangle by multiplying the shorter and longer sides:
Area = shorter side x longer side
= 9 cm x 12 cm
= 108 cm^2
Hence, the area of the rectangle is 108 cm^2.