Question

The length of the diagonal of a rectangle is 10 cm and its area is 62.5 cm . Find the sum of its length and breadth. ​

Answer 1

Answer:

Sum of its length and breadth is 15 cm.

Step-by-step explanation:

Given :-

• The length of the diagonal of a rectangle is 10 cm and its area is 62.5 cm².

To find :-

• The sum of its length and breadth.

Solution :-

Let the length of the rectangle be x cm and the breadth of the rectangle be y cm.

Formula used :

${\boxed{\sf{Diagonal\:of\: rectangle=\sqrt{length^2+breadth^2}}}}$

According to the 1st condition,

$\to \sf \: \sqrt{ {x}^{2} + {y}^{2} } = 10 \\ \\ \to \sf \: {x}^{2} + {y}^{2} = {10}^{2} \\ \\ \to \sf \: {x}^{2} + {y}^{2} = 100...........(i)$

According to the 2nd condition,

xy = 62.5..............(ii)

Now take eq(i) and put xy=62.5 from eq (ii).

→ x² + y² = 100

→ (x+y)² - 2xy = 100

→ (x+y)² - 2×62.5 = 100

→ (x+y)² - 125 = 100

→ (x+y)² = 100+125

→ (x+y)² = 225

→ x+y = √225

→ x+y = 15

Therefore, the sum of its length and breadth is 15 cm.