Question

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

(a) 100 cm²
(b) 110 cm²
(c) 120 cm²
(d) 150 cm²

Answer 1

(c) 120 cm²
Let the length of the rectangle be x cm and the breadth be y cm.
Area of the rectangle = xy cm²
Perimeter of the rectangle = 2( x + y) = 46 cm (given)
⇒ 2( x + y) = 46
⇒ ( x + y) = $\frac{46}{2}$ cm = 23 cm
Diagonal of the rectangle = $\sqrt{x^2+y^2}$ = 17 cm
⇒ $\sqrt{x^2+y^2}$ = 17
Squaring both the sides, we get:
⇒ x² + y² = (17)²
⇒ x² + y² = 289
Now, (x² + y²) = ( x + y)² - 2xy
⇒ 2xy = ( x + y)² - (x² + y²)
= (23)² - 289
= 529 - 289 = 240
∴ xy = $\frac{240}{2}$ cm² = 120 cm²