One side of a rectangle is 4 m longer than four times another side. The area of the rectangle is 224 m². Find the length of the shorter side. m

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Hampo asked Feb 25, 2023

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17 votes

One side of a rectangle is 4 m longer than four times another side. The area of the rectangle is 224 m².

Find the length of the shorter side.
m

Mathematics
college

Hampo asked Feb 25, 2023

by Hampo

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1 Answer

15 votes

Let the another side be x m.

Therefore, the longer side = (4 + 4x) m.

Now,

${\sf{→x * (4 + 4x) = 224 \\ →4x + 4x {}^(2) - 224 = 0 \\→ x {}^(2) + x - 56 = 0 \\ →x {}^(2) + 8x - 7x - 56 = 0 \\ →x(x + 8) - 7(x + 8) = 0 \\ →(x - 7)(x +8 ) = 0 \\ →x = 7 \: or \: x = - 8 \\ \\ length \: cannot \: be \: negative \\ possible \: solution \: (x) = 7}}$

Length of shorter side = x = 7 metres.

${\sf{answer\: \\ss}}$