Find the perimeter and area of the rectangle whose breadth is 8 cm and

1.	Find the perimeter and area of the rectangle whose breadth is 8 cm and a diagonal is 17 cm.
Answer» Given BREADTH of Rectangle ⇒ 8 cm Diagonal of Rectangle ⇒ 17 cm _________________________________ To Find Perimeter of Rectangle Area of Rectangle _________________________________ Solution Breadth = 8 cm Diagonal = 17 cm Length = x cm Using Pythagorean Theorem we will find the length of the rectangle. The hypotenuse would be 17 cm. Pythagorean Theorem ⇒ Base² + Height² = Hypotenuse² ⇒ (x)² + (8)² = (17)² ⇒ x² + 64 = 289 ⇒ x² + 64 - 64 = 289 - 64 ⇒ x² = 225 ⇒ x = √225 ⇒ x = 15 ∴ The length is 15 cm. Perimeter of rectangle ⇒ 2 (Length + Breadth) Length ⇒ 15 cm Breadth ⇒ 8 cm Perimeter of Rectangle ⇒ 2 (15 + 8) ⇒ 2 (23) ⇒ 46 cm ∴ Perimeter of Given Rectangle is 46 cm. Area of Rectangle ⇒ Length × Breadth Length ⇒ 15 cm Breadth ⇒ 8 cm Area of Rectangle ⇒ 15 × 8 ⇒ 120 cm² ∴ Area of Given Rectangle is 120 cm². _________________________________

Find the perimeter and area of the rectangle whose breadth is 8 cm and a diagonal is 17 cm.

Answer»

Given

BREADTH of Rectangle ⇒ 8 cm
Diagonal of Rectangle ⇒ 17 cm

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To Find

Perimeter of Rectangle
Area of Rectangle

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Solution

Breadth = 8 cm

Diagonal = 17 cm

Length = x cm

Using Pythagorean Theorem we will find the length of the rectangle. The hypotenuse would be 17 cm.

Pythagorean Theorem ⇒ Base² + Height² = Hypotenuse²

⇒ (x)² + (8)² = (17)²

⇒ x² + 64 = 289

⇒ x² + 64 - 64 = 289 - 64

⇒ x² = 225

⇒ x = √225

⇒ x = 15

∴ The length is 15 cm.

Perimeter of rectangle ⇒ 2 (Length + Breadth)

Length ⇒ 15 cm

Breadth ⇒ 8 cm

Perimeter of Rectangle ⇒ 2 (15 + 8)

⇒ 2 (23)

⇒ 46 cm

∴ Perimeter of Given Rectangle is 46 cm.

Area of Rectangle ⇒ Length × Breadth

Length ⇒ 15 cm

Breadth ⇒ 8 cm

Area of Rectangle ⇒ 15 × 8

⇒ 120 cm²

∴ Area of Given Rectangle is 120 cm².

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