Question

If the length of the top of a rectangle is 15 inches more than its width and the area is 1350 square inches. Find the dimensions.

Answer 1

Given :-

Length is 15 inches more than its breadth.

Area is 1350 square inches

To find :-

Breadth of the rectangle

Soln :-

Let breadth is x

Then, Length = x + 15

Area = L × B

( x ) × ( x + 15 )

( x × x ) + ( x × 15 )

x² + 15x

But, the area is given which is 1350 square inches

So,

x² + 15x = 1350

x² + 15x - 1350 = 0

( Given expression is x² + 15x - 1350 )

Find two numbers whose sum equals to 15 and product equals to - 1350

So, those no.s are 45 and -30

So, x² + 45x - 30x - 1350 = 0

x( x + 45 ) - 30( x + 45 ) = 0

( x + 45 ) ( x - 30 ) = 0

Here, x - 30 = 0

So, x = 30 [ This is the breadth ]

Therefore, Length = 30 + 15 which is 45

Answer 2

The dimensions of the top of a rectangle is length 45 square inches and breadth 30 square inches.

Given:

Length =  15 inches more than its breadth.

Area of the top of a rectangle = 1350 square inches

To find: Dimensions of the top of the rectangle

Formula used:

Area of a rectangle = Length × Breadth

Solution:

Step 1: Substitute the value of length and breadth:

Let breadth is x then Length = (x + 15)

Area of a top of the rectangle = L × B

Area of a top of the rectangle = ( x ) × (x + 15)

Area of a top of the rectangle = (x × x) + (x × 15)

Area of a top of the rectangle =  x² + 15x

x² + 15x = 1350

[Given : Area = 1350 square inches]

$\bf x^{2} + 15x - 1350 = 0$

Step2: Find the dimensions:

$\bf x^{2} + 15x - 1350 \\\\x^{2} + 45x - 30x - 1350 = 0$

[By middle-term splitting method]

$\bf x( x + 45 ) - 30( x + 45 ) = 0 \\\\( x + 45 ) ( x - 30 ) = 0 \\\\(x - 30) = 0 \or \ (x + 45) = 0$

x = 30 or x = - 45

Breadth can't be negative

So, Breadth, x = 30 then Length = x + 15 = 30 + 15 = 45

Hence, the length and breadth of a top of a rectangle is 45 square inches and 30 square inches.

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