Question

Help me please, find the area of a rectangle, if its perimeter is 20cm and its diagonal is 8cm.

here are answers if needed too:
1) 18cm²
2) 12cm
3) 30cm²
4) 24cm²​

Answer 1

Answer:

1)18cm²

Step-by-step explanation:

Let length be l and breadth be b

Diagonal of rectangle = √(l²+b²) = 8 ...(i)

Perimeter of rectangle = 2(l+b) = 20

• Divide both sides by 2 to get (l+b) = 20/2 = 10 cm ...(ii)

We know Area of rectangle = l*b

From equation (i) square both sides:

• l²+b² = 8² = 64

We know that (l²+b²) = (l+b)²-2lb

• (l+b)²-2lb = 64

Put the value of (l+b) = 10 from equation (ii)

• (10)²-2lb = 64

Subtract 8² from both sides:

• 10²-64-2lb = 0

Add 2lb to both sides:

• 100-64 = 36 = 2lb

Divide both sides by 2:

• 36/2 = 18 = l*b

However,Area of rectangle = l*b

So the area of the rectangle = 18 cm²