Question

A rectangle has a length of X +5 and a width of X -5 and has an area of 15 square units find the length and width of the rectangle.

asked Mar 28, 2023 135k views

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Sumit Jha · Answer 1 · 2023-04-03T09:25:45+0000

Given :-

Length of rectangle = x + 5
width of rectangle = x - 5
Area of rectangle = 15 unit²

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To find:-

Actual length and width of rectangle

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Solution:-

So to find actual length and width of rectangle, we need to find value of x.

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we know:-

$\bigstar \boxed{ \rm Area~of \: rectangle = length * width}$

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So:-

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$\hookrightarrow \sf Area~of \: rectangle = length * width \\$

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$\hookrightarrow \sf 15=(x + 5)(x - 5) \\$

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$\hookrightarrow \sf 15=x (x - 5) +5(x - 5)\\$

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$\hookrightarrow \sf 15=x^2 - 5x +5(x - 5)\\$

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$\hookrightarrow \sf 15=x^2 - 5x +5x - 25\\$

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$\hookrightarrow \sf 15=x^2 - \cancel {5x} +\cancel {5x} - 25\\$

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$\hookrightarrow \sf 15=x^2 -0 - 25\\$

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$\hookrightarrow \sf 15=x^2 - 25\\$

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$\hookrightarrow \sf 15 + 25=x^2 \\$

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$\hookrightarrow \sf 15 + 25=x^2 \\$

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$\hookrightarrow \sf 40=x^2 \\$

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$\hookrightarrow \sf x^2 = 40\\$

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$\hookrightarrow \sf x = √(40)\\$

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$\hookrightarrow \sf x = √(2 * 2 * 10)\\$

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$\hookrightarrow \sf x = 2 √(10)\\$

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$\hookrightarrow \sf x = 2 * 3.16\\$

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$\hookrightarrow \sf x = 2 * 3.16\\$

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$\hookrightarrow \bf x = 6.32(approx)\\$

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Length = x + 5
Length = 6.32 + 5
Length = 11.32 (units)

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Breadth = x - 5
Breadth = 6.32 - 5
Breadth = 1.32 (units)

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Given :-

To find:-

Solution:-

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