A rectangle is 72cm³in area and perimeter is 34cm. Find it's length and breadth
Let's assume the length of the rectangle is L cm and the breadth is B cm.
We know that the area (A) of a rectangle is given by A = length * breadth.
Given that the area is 72 cm², we can write the equation as:
72 = L * B ---(1)
We also know that the perimeter (P) of a rectangle is given by P = 2 * (length + breadth).
Given that the perimeter is 34 cm, we can write the equation as:
34 = 2 * (L + B) ---(2)
From equation (2), we can simplify as:
17 = L + B
Let's substitute the value of B in equation (1) using L + B = 17:
72 = L * (17 - L)
72 = 17L - L²
Rearranging the equation and making it a quadratic equation:
L² - 17L + 72 = 0
We can factorize the quadratic equation as:
(L - 8)(L - 9) = 0
Therefore, L = 8 or L = 9.
Now, we can substitute each value of L back into equation (2) to find B.
When L = 8:
17 = 8 + B
B = 17 - 8
B = 9
When L = 9:
17 = 9 + B
B = 17 - 9
B = 8
So, the possible dimensions of the rectangle are:
Length = 8 cm and Breadth = 9 cm
or
Length = 9 cm and Breadth = 8 cm.