The perimeter of a triangle is 44cm. The area of the rectangle is 117cm2. Find the length of the shorter side of the rectangle. Help please

Shorter side = 9 cm

The perimeter of a rectangule is 44cm. The area of the rectangle is 117cm2. Find the length of the shorter side of the rectangle.

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

55

step-by-step explanation: