Question

2. The length of a rectangle is 16 cm and the length of its diagonal is 20 cm. Find
the area of the rectangle​

Answer 1

Answer:

• Area of rectangle is 192 cm².

Step-by-step explanation:

Given :-

• Length of rectangle is 16 cm.
• Diagonal of rectangle is 20 cm.

To find :-

• Area of rectangle.

Solution :-

• First we will find breadth of rectangle because we do not have breadth of rectangle for area.

Let, rectangle be ABCD.

BC be length of rectangle.

AC be diagonal of rectangle.

And, AB be breadth of rectangle.

We know,

All angles of rectangle are of 90°.

So,

∆ABC is a right angle right. ∆ABC will right angled from B.

By Pythagoras theorem :

• Perpendicular² = Hypotenuse² - Base²

Perpendicular = AB

Hypotenuse = AC = 20 cm.

Base = BC = 16 cm.

Put all values in Pythagoras theorem :

$\longrightarrow$ (AB)² = (AC)² + (BC)²

$\longrightarrow$ (AB)² = (20)² + (16)²

$\longrightarrow$ (AB)² = 400 - 256

$\longrightarrow$ (AB)² = 144

$\longrightarrow$ AB = √144

$\longrightarrow$ AB = 12

Thus,

AB is 12 cm.

AB is perpendicular of ∆ABC and AB is breadth of rectangle ABCD.

So, Breadth of rectangle is 12 cm.

We know,

Area of rectangle = Length × Breadth

$\longrightarrow$ Area = 16 × 12

$\longrightarrow$ Area = 192

Therefore,

Area of rectangle is 192 cm².

Answer 2

Answer:

Given :-

• The length of a rectangle is 16 cm and the length of its diagonal is 20 cm.

To Find :-

• What is the area of the rectangle.

Formula Used :-

By using Phythagorus Theorem we know that,

★ (AC)² = (AB)² + (BC)² ★

To find area of the rectangle we know that,

✪ Area of the rectangle = Length × Breadth ✪

Solution :-

Let, BC or breadth be b

Then, AB or length is 16 cm

And, the AC or diagonal will be 20 cm

Now, according to the question by using the formula we get,

⇒ (AC)² = (AB)² + (BC)²

⇒ (20)² = (16)² + (b)²

⇒ (b)² = (20)² + (16)²

⇒ (b)² = 400 - 256

⇒ (b)² = 144

⇒ b = √144

➠ b = 12 cm

Hence, the breadth is 12 cm

Now, we have to find the area of the rectangle,

We get,

• Length = 16 cm
• Breadth = 12 cm

According to the question by using the formula we get,

↦ Area = Length × Breadth

↦ Area = 16 cm × 12 cm

➦ Area = 192 cm²

∴ The area of the rectangle is 192 cm² .