2. The length of a rectangle is 8 cm more than its width. If its perimeter is 56 cm, find itslength and its area.
Answers
Assume that the breadth of the rectangle is x cm and width is y cm.
As per given condition,
The length of a rectangle is 8 cm more than its width.
⇒ Length = 8 + Width/Breadth
⇒ x = 8 + y .............(1st equation)
Also given that, perimeter of rectangle is 56 cm.
We know that,
Perimeter of rectangle = 2(length + width)
Substitute the known values in the above formula,
→ 56 = 2(x + y)
Substitute value of x from (1st equation)
→ 56 = 2(8 + y + y)
→ 56 = 2(8 + 2y)
→ 56 = 16 + 4y
→ 56 - 16 = 4y
→ 40 = 4y
Divide by 4 on both sides,
→ 40/4 = 4y/4
→ 10 = y
(Width of rectangle is 10 cm)
Now, substitute value of y in (1st equation)
→ x = 8 + 10
→ x = 18
(Length of rectangle is 18 cm)
Area of rectangle = Length × Width
= 18 × 10
= 180 cm²
Therefore, the length of rectangle is 18 cm, width is 10 cm and area is 180 cm².