# What will be the Area of the Rectangle? If

If the diagonal of a rectangle is 17 cm long and the perimeter of the rectangle is 46 cm, then the area of the rectangle is:

- 120 cm
^{2} - 112 cm
^{2} - 132 cm
^{2} - 289 cm
^{2}

**Answer: (1) 120 cm ^{2}**

**Explanation:-**

Let the length of a rectangle = X m & width of the rectangle = Y m.

**Formula-**

**Perimeter of a rectangle = 2 (l + b)**

**Where, l = length of the rectangle & b = breadth of the rectangle**

Then, 2 (X + Y ) = 46

X + Y = 46/2

X + Y = 23

**Formula-**

**diagonal of the rectangle = X ^{2} + Y ^{2}**

**Where, X & Y are the length & breadth of the rectangle.**

Then, X^{2} + Y^{2} = 17^{2 } = 289

Now, (X + Y )^{2} = 23^{2}

X^{2} + Y^{2} + 2 X Y = 529

289 + 2 X Y = 529

2 X Y = 529 – 289

X Y = 240/2

X Y = 120

The area of the rectangle = X Y = 120 cm^{2}

Hence, the answer is (1) 120 cm^{2}