Question

plzz answer this question...​

Answer 1

Answer:

a) xy = 60 cm² and x² + y² = 169 cm²

b) x + y = 17 cm and x - y = 7 cm

c) x = 12 cm and y = 5 cm

Step-by-step explanation:

Given:-

• Diagonal of the rectangle = 13 cm
• Area of the rectangle = 60 cm²

To find:-

• (a) Values of xy and x² + y²
• (b) Values of x + y and x - y
• (c) Values of x and y

Solution:-

a)  Values of xy and x² + y²

Area of the rectangle = Length × Breadth

⇒60 cm² = x × y

⇒ xy = 60 cm²

x, y, and 13 cm are sides of a right triangle and 13 cm is the hypotenuse

∴ x² + y² = (13 cm)²

⇒ x² + y² = 169 cm²

Answer⇒ xy = 60 cm² and x² + y² = 169 cm²

b) Values of x + y and x - y

(x + y)² = x² + y² + 2xy

           = (x² + y²) + 2(xy)

           = (169 cm²) + 2(60 cm²)

           = 169 cm² + 120 cm²

           = 289 cm²

⇒(x + y)² = 289 cm²

⇒ x+ y = $\sqrt{(x + y)^{2} }$

           = $\sqrt{289 cm^{2} }$

           = 17 cm

⇒ x+ y = 17 cm

(x - y)² = x² + y² - 2xy

           = (x² + y²) - 2(xy)

           = (169 cm²) - 2(60 cm²)

           = 169 cm² - 120 cm²

           = 49 cm²

⇒(x - y)² = 49 cm²

⇒ x - y = $\sqrt{(x - y)^{2} }$

           = $\sqrt{49 cm^{2} }$

           = 7 cm

⇒ x - y = 7 cm

Answer⇒ x + y = 17 cm and x - y = 7 cm

c) Values of x and y

x + y = 17 cm and x - y = 7 cm

(x + y) + (x - y) = (17 cm) + (7 cm)

⇒ x + y + x - y = 17 cm + 7 cm

⇒ 2x = 24 cm

⇒ x = 24 cm ÷ 2

⇒ x = 12 cm

Putting x = 12 cm in x + y = 17 cm, we get

x + y = 17

⇒12 cm + y = 17 cm

⇒ y = 17 cm - 12 cm

⇒ y = 5 cm

Answer⇒ x = 12 cm and y = 5 cm

More to know:-

• Area of a rectangle = Length × Breadth
• Area of a square = (Side)², also Area of a Square = $\frac{1}{2}$ × (Diagonal)²

• Area of a parallelogram = Base × Height

• Area of a rhombus = $\frac{1}{2}$ × (Product of diagonals)

• Area of a trapezium = $\frac{1}{2}$  × (Sum of parallel sides) × (distance between them)

• Area of a triangle = $\frac{1}{2}$ × Base × Height, also                                           Area of a triangle = $\sqrt{s(s -a)(s - b)(s - c)}$, where s is the semi-perimeter and a, b, and c are the sides of the triangle.

I hope that this helped you

Mark my answer as the brainliest and follow me