Math, asked by deucalionguarin, 6 months ago

marilyn has a photograph which is 8 cm longer than it is width and its area is 33cm². what are the dimention of the photograph?

Answers

Answered by bhagyashreechowdhury

Given:

Marilyn has a photograph which is 8 cm longer than it's width and its area is 33cm²

To find:

What is the dimension of the photograph?

Solution:

Let's assume,

"L" → the length of the photograph

"W" → the width of the photograph

So, according to the question, we have

Length of the photograph is 8 cm more than its width

∴ L = W + 8 ..... (i)

The area of the photograph that Marilyn has = 33 cm²

We know that,

$\boxed{\bold{Area\:of\:a\:rectangle = length\times width}}$

Now, we get an equation as,

L × W = 33

on substituting from (i), we get

⇒ (W + 8) × W = 33

⇒ W² + 8W = 33

⇒ W² + 8W - 33 = 0

⇒ W² + 11W - 3W - 33 = 0

⇒ W(W + 11) - 3(W + 11) = 0

⇒ (W + 11)(W - 3) = 0

⇒ W = -11 or W = 3

since the width cannot be negative, therefore ignoring the negative value of W

⇒ W = 3 cm ← length of the photograph

Substituting the value of W in eq. (i), we get

L = W + 8

⇒ L = 3 + 8

⇒ L = 11 cm ← width of the photograph

Thus, the dimension of the photograph is → 11 cm × 3 cm.

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