Question

$\huge \fbox \red{❥ Question}$


The diagonal of a rectangular field is 60 metres more than the shorter side. If the longer side is 30 metres more than the shorter side, find the sides of the field.




(REQUIRED QUALITY ANSWER)​

Answer 1

Required Answer:-

Given:

• The diagonal of a rectangular field is 60 metres more than shorter side.
• The longer side is 30 metres more than shorter side.

To find:

• The length of each sides of the field.

Solution:

Let ABCD be the rectangular field where,

• Length = AB
• Breadth = AD
• Diagonal = AC

Let the breadth of the rectangle be x m.

So,

➡ Breadth = x m.

➡ Diagonal = (60 + x) m.

➡ Length = (30 + x) m.

By Pythagoras Theorem,

➡ (x + 60)² = x² + (x + 30)²

➡ x² + 120x + 3600 = x² + x² + 60x + 900

➡ x² + 60x + 900 - 120x - 3600 = 0

➡ x² - 60x - 2700 = 0

Now, solve for x.

➡ x² - 90x + 30x - 2700 = 0

➡ x(x - 90) + 30(x - 90) = 0

➡ (x + 30)(x - 90) = 0

By zero product rule, we get,

➡ x = -30 or 90

But length of sides cannot be negative. So,

➡ x = 90 m.

Hence,

➡ Breadth = 90 m.

➡ Length = 30 + 90 m = 120 m.

➡ Diagonal = 60 + 90 m = 150 m.

★ Hence, the length and breadth of the rectangular field are 90 m and 120 m.

Answer:

• The length and breadth of the rectangular field are 90 m and 120 m.