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Darya [45]
3 years ago
15

How do we figure this out

Mathematics
1 answer:
lisov135 [29]3 years ago
8 0

Answer:

Pair 1: 10 cm and 2 cm. and the sum is 12 cm.

Pair 2: 20 cm and 4 cm. and the sum is 24 cm.

Step-by-step explanation:

Area of a rectangle is given by A = LW, where L is the length and W is the width of the rectangle.

Pair 1:

For the first rectangle W = 4 cm and A = 40 sq, cm

Then L = \frac{A}{W} = \frac{40}{4} = 10 cm.

For the second rectangle W = 4 cm and A = 8 sq, cm

Then L = \frac{A}{W} = \frac{8}{4} = 2 cm.

Therefore, the sum of two unknown lengths = 10 + 2 = 12 cm. (Answer)

Pair 2:

For the first rectangle W = 4 cm and A = 80 sq, cm

Then L = \frac{A}{W} = \frac{80}{4} = 20 cm.

For the second rectangle W = 4 cm and A = 16 sq, cm

Then L = \frac{A}{W} = \frac{16}{4} = 4 cm.

Therefore, the sum of two unknown lengths = 20 + 4 = 24 cm. (Answer)

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\text{L.H.S}\\\\=\begin{vmatrix} 1 & bc& b+c\\ 1 & ca& c+a\\ 1 &ab&a+b\end{vmatrix}\\\\\\=\begin{vmatrix} 1 & bc& b+c-(a+b+c)\\ 1 & ca& c+a-(a+b+c)\\ 1 &ab&a+b-(a+b+c)\end{vmatrix}~~~~~~~~~~~~~~~;c_3\rightarrow c_3 -(a+b+c)c_1\\\\\\=\begin{vmatrix} 1 & bc& -a\\ 1 & ca& -b\\ 1 &ab&-c\end{vmatrix}\\\\\\=\dfrac 1{abc}\begin{vmatrix} a & abc& -a^2\\ b & abc& -b^2\\ c &abc&-c^2\end{vmatrix}\\\\\\=-\dfrac {abc}{abc}\begin{vmatrix} a & 1& a^2\\ b & 1& b^2\\ c &1&c^2\end{vmatrix}\\

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