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cricket20 [7]
3 years ago
6

A rectangle has a perimeter of 110 inches. The rectangle' s length is five more than twice the width.

Mathematics
1 answer:
77julia77 [94]3 years ago
4 0

Answer:

Length is 38\frac{1}{3} inches

Width is 16\frac{2}{3} inches

Step-by-step explanation:

Let the width be x inches

The length will be 2x + 5 inches

The perimeter is 110 inches

Perimeter is given by (2 × length) + (2 × width)

2(2x + 5) + 2x = 110 inches

4x + 10 + 2x = 110 inches

6x = 100 inches

x (width) = 100/6 = 16\frac{2}{3} inches

Length = 2(100/6) + 5 = 38\frac{1}{3} inches.

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\large\underline{\sf{Solution-}}

\sf  \longmapsto x + y = 7 \: \: - - - (i)

\sf  \longmapsto 3x - 2y = 11 \: \: - - - (ii)

<u>By first equation,</u>

\sf  \longmapsto x + y = 7

\sf  \longmapsto x = 7 - y

<u>Now, we can find the original value of y.</u>

\sf \longmapsto 3x - 2y = 11

\sf  \longmapsto 3(7 - y) - 2y = 11

\sf  \longmapsto 21 - 3y - 2y = 11

\sf  \longmapsto 21 - 5y = 11

\sf  \longmapsto - 5y = 11 - 21

\sf  \longmapsto - 5y =  - 10

\sf  \longmapsto y = \dfrac{ - 10}{ - 5}

\sf  \longmapsto y = 2

<u>Now, we can find the original value of x.</u>

\sf  \longmapsto x + y = 7

\sf  \longmapsto x + 2 = 7

\sf  \longmapsto x = 7 - 2

\sf  \longmapsto x = 5

Therefore, the values of x and y are 5 and 2 respectively.

8 0
2 years ago
Read 2 more answers
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