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lukranit [14]
3 years ago
11

the area of a rectangle is 90 in2^. the ratio of the length to the width is 5:2. find the length and the width

Mathematics
1 answer:
-BARSIC- [3]3 years ago
4 0

Length and width of rectangle is 15 inches and 6 inches respectively

<h3><u>Solution:</u></h3>

Given that area of a rectangle is 90 square inch

Ratio of length to the width = 5: 2.

Need to determine length and width of rectangle.  

As ratio of length to the width is 5 : 2

Lets assume length of rectangle = 5x inches and width of rectangle = 2x inches.

<em><u>The formula for area of rectangle is given as:</u></em>

\text { Area of rectangle }=\text { length of rectangle } \times \text { width of rectangle}

Substituting the given value of area of rectangle and assumed value of length and width of rectangle we get:

\begin{array}{l}{90=5 x \times 2 x} \\\\ {=>90=10 x^{2}}\end{array}

On solving the above expression for x we get

\begin{array}{l}{=>\frac{90}{10}=x^{2}} \\\\ {=>x^{2}=9} \\\\ {=>x=\sqrt{9}=3}\end{array}

\begin{array}{l}{\text { Length of rectangle }=5 \times x=5 \times 3=15 \text { inches }} \\\\ {\text { Width of rectangle }=2 \times} x=2 \times} 3=6 \text { inches }}\end{array}

Hence length and width of rectangle is 15 inches and 6 inches.

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I. m = 2401

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We'll begin by obtaining (n+1) ∆ y. This can be obtained as follow:

x ∆ y = x² − 2xy + y²

(n+1) ∆ y = (n+1)² – 2(n+1)y + y²

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((n+1) ∆ y)/n = 1/n[(n – y + 2)(n – y) + 1]

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