Question

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

$\huge{\bold{\boxed{\mathtt{\red{Given\::-}}}}}$

• Length of Rectangle = 16 cm
• Length of Diagonal = 20 cm

$\huge{\bold{\boxed{\mathtt{\purple{To\:Find\::-}}}}}$

• Area of Rectangle

$\huge{\bold{\boxed{\mathtt{\orange{Solution\::-}}}}}$

Length = 16cm

Diagonal = 20cm

Let BC = 'x'

Since, ∆ ABC is right angled triangle,

∴ By Pythagoras theorem :-

$\large{\boxed{\mathtt{\green{(H)²\:=\:(P)²+(B)²}}}}$

Here,

• H = Hypotenuse = AC = 20cm
• B = Base = AB = 16cm
• P = prependicular = BC = 'x' cm

Substituting the value in the above formula, we get :-

$\mapsto{\bold{(AC)²\:=\:(BC)²+(AB)²}}$

$\mapsto{\bold{(20)²\:=\:(x)²+(16)²}}$

$\mapsto{\bold{400\:=\:x²+256}}$

$\mapsto{\bold{400-256\:=\:x²}}$

$\mapsto{\bold{144\:=\:x²}}$

$\mapsto{\bold{x\:=\: \sqrt{144}}}$

$\huge{\boxed{\mathfrak{\color{lime}{x\:=\:12cm}}}}$

Now,

Length = 16cm

Breadth = x = 12cm

$\large{\boxed{\mathtt{\color{aqua}{Area\:=\:L×B}}}}$

Here,

• L = length = 16cm
• B = breadth = 12cm

Substituting the value in tha above formula, we get :-

$\mapsto{\bold{Area\:=\:16×12}}$

$\huge{\boxed{\mathtt{\color{Indigo}{Area\:=\:192cm²}}}}$

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