Required Answer:
Shorter side = 9 cm
Question:
The perimeter of a rectangule is 44cm. The area of the rectangle is 117cm2. Find the length of the shorter side of the rectangle.
Let:
- Length rectangle be a.
- Width of rectangle be b.
To find?
- Length of the shorter side of the rectangle.
Given:
- Perimeter of rectangle = 44cm
- Area of rectangle = 117cm²
Answer :
A/Q
Perimeter of rectangle = 44cm
We know:
p=2(L+B)
.°. ⇒44 =2(a+b)
⇒44 /2 =a+b
⇒22=a+b
So:
a=22-b
b=22-a
Now Let's put values in formula of Area
A/Q
Area of rectangle = 117cm²
We know:
Area =L×B
.°.117=ab
Put value of b in this equation
⇒117=a(22-a)
⇒117=22a-a²=0
⇒a-22a²+117=0
⇒(a- 9)(a- 13) = 0
.°. a=9
a=13cm
Let's put value of a as 13 to find b
⇒b=22-a
⇒b=22-13
⇒b=9cm
So the side having 9cm is shorter i.e. b