Question

The width of a rectangle is 6cm and its diagonal is 10cm.What is its perimeter ?
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Answer 1

Answer:

The perimeter = 28m

Step-by-step explanation:

Width of a rectangle is 6cm

Its Diagonal is 10cm

By Pythagorean theorem:

Its length squared = $10^{2} - 6^{2}$ = 100 - 36 = 64 = $8^{2}$

∴ Length = 8cm.

∴ The perimeter = 2(8 + 6) = 28m  

Answer 2

Answer :-

• Perimeter of the rectangle is 28cm.

Given :-

• The width of a rectangle is 6cm and its diagonal is 10cm.

To Find :-

• Perimeter of the rectangle.

Solution :-

Let ABCD be the rectangle.

• Diagonal AC = 10cm
• Breadth BC = 6cm
• Length AB = ?

From Pythagoras theorem

As we know that

AC² = AB² + BC²

Put the values in the formula

⇒ (10)² = (AB)² + (6)²

⇒ 100 = AB² + 36

⇒ AB² = 100 - 36

⇒ AB² = 64

⇒ AB = √64

⇒ AB = 8cm

→ Length = 8cm

As we know that

Perimeter of the rectangle = 2 (l + b)

Where

• l = length
• b = breadth

Put the values in the formula

⇒ Perimeter = 2 (8 + 6)

⇒ Perimeter = 2 × 14

⇒ Perimeter = 28cm

Hence, the perimeter of the rectangle is 28cm.