A rectangle is 5cm longer that it is broad. It perimeter is 26cm. Find the length and breadth of the rectangle
2 w + 2 (w+5) = 26
2 w + 5 = 13
2 w = 8
w = 4
w+5 = 9
To find the length and breadth of the rectangle, we can set up a system of equations based on the information given.
Let:
L be the length of the rectangle
B be the breadth of the rectangle
According to the problem, the rectangle is 5cm longer than its breadth, so we can write the equation:
L = B + 5 -- Equation 1
The perimeter of a rectangle is given by the formula:
Perimeter = 2 × (Length + Breadth)
Given that the perimeter of the rectangle is 26 cm, we can write the equation:
26 = 2 × (L + B) -- Equation 2
Now we have a system of two equations with two unknowns:
Equation 1: L = B + 5
Equation 2: 26 = 2 × (L + B)
To solve this system of equations, we can substitute Equation 1 into Equation 2:
26 = 2 × ((B + 5) + B)
26 = 2 × (2B + 5)
26 = 4B + 10
4B = 26 - 10
4B = 16
B = 16 / 4
B = 4
Now, substitute the value of B back into Equation 1 to find the length:
L = B + 5
L = 4 + 5
L = 9
Therefore, the length of the rectangle is 9 cm and the breadth is 4 cm.