Question

The length of the diagonal of a rectangular playground is 125m and the length of one side is 75m . Find the length of the other side

Answer 1

Question

The length of the diagonal of a rectangular playground is 125m and the length of one side is 75m . Find the length of the other side

Solution

Given:-

• The length of the diagonal of a rectangular playground is 125m.
• The length of one side is 75m.

Find:-

• Length of other side.

Explanation

In graph Rectangular playground is ABCD .

Where, AC is diagonal of ABCD .

Then, we find here two right triangle ,

ABC & ADC .

So, we take Any right triangle ABC .

Here,

• AB = CD & AD = BC
• AC = Hypotenuse = 125 m
• AB = Length of Rectangular playground = 75 m

Using Pythagoras's theorem

☛ (Hypotenuse )² = (perpendicular )²+(Base)².

➠ AC² = AD² + AB²

➠ 125² = AD² + 75²

➠ AD² = 15,625 - 5,625

➠ AD² = 10,000

➠ AD = √(10,000)

➠AD = 100 m

Thus

• Other length of rectangular playground will be (AD) = 100 m

Or,

All side will be

• AB = CD = 75 m
• AD = BC = 100 m

________________

Answer 2

✬ Length of other side = 100 m ✬

Step-by-step explanation:

Given:

• Measure of diagonal of rectangular playground us 125 m.
• Length of one side of rectangular playground is 75 m.

To Find:

• What is the length of the other side of rectangular playground ?

Solution: Let ABCD be a rectangular playground in which :-

• AB = DC = 75 m ( side of ABCD )
• BD = 125 m ( diagonal of ABCD )

• We know that the opposite sides of rectangle are equal and measure of each angle is of 90° •

➪ In ∆BAD

• AB = Base
• DA = Perpendicular
• BD = Hypotenuse

•Applying Pythagoras Theorem in ∆BAD•

★Hypotenuse²=Base²+Perpendicular²★

$\implies{\rm }$ (BD)² = (AB)² + (DA)²

$\implies{\rm }$ (125)² = (75)² + (DA)²

$\implies{\rm }$ 15625 = 5625 + DA²

$\implies{\rm }$ (15625 – 5625) = DA²

$\implies{\rm }$ 10000 = DA²

$\implies{\rm }$ √10000 = DA²

$\implies{\rm }$ 100 m = DA

Hence, The measure of other side of rectangular playground ABCD is 100 m.

_________________________

➨ Area of Rectangle = (Length x Breadth)sq units

➨ Perimeter = 2 ( Length + Breadth )

➨ Opposite sides of a rectangle are equal.

➨ Diagonals of a rectangle are equal.

➨ All angles of rectangle measure 90°.