Question

The length and breadth of a rectangle is 18 cm , 12 cm . If the length and breadth is increased by x cm , the area becomes 432 cm square . Then find the value of x .​

Answer 1

✬ Value of x = 6 cm ✬

Step-by-step explanation:

Given:

• Length of rectangle is 18 cm.
• Breadth of rectangle is 12 cm.
• After increasing length and breadth by x area becomes 432 cm².

To Find:

• Value of x ?

Solution: When we increase length & breadth by x then -

• New length = (18 + x) cm
• New breadth = (12 + x) cm

As we know that

★ Ar. of Rectangle = Length × Breadth ★

A/q

• New area becomes 432 cm².

➮ (18 + x) (12 + x) = 432

➮ 216 + 18x + 12x + x² = 432

➮ 30x + x² = 432 – 216

➮ 30x + x² = 216

➮ x² + 30x – 216 = 0

Now using middle term splitting method

➯ x² + 36x – 6x – 216 = 0

➯ x(x + 36) – 6 (x + 36) = 0

➯ (x + 36) (x – 6) = 0

➯ (x + 36) = 0 or (x – 6) = 0

➯ x = –36 or x = 6

• We will take positive value of x.

Hence, value of x will be 6 cm.

[ Verification ]

• New length = 18 + 6 = 24 cm
• New breadth = 12 + 6 = 18 cm

$\implies{\rm }$ Length × Breadth = 432 cm²

$\implies{\rm }$ (24 × 18)cm = 432 cm²

$\implies{\rm }$ 432 cm² = 432 cm²

$\large\bold{\texttt {Verified }}$

Answer 2

Refer the above attachment....Hope u helpful