Can someone help me with this problem? Thank you!

Question

asked Feb 22, 2023 87.1k views

1 Answer

Faisal Ijaz · Answer 1 · 2023-02-28T16:11:14+0000

$\qquad\qquad\huge\underline{{\sf Answer}}$

Since, the Area of smaller rectangle is 35,

Let's calculate it's length ~

$\qquad \sf  \dashrightarrow \:a = l \cdot w$

$\qquad \sf  \dashrightarrow \:35 = l \cdot5$

$\qquad \sf  \dashrightarrow \:l = 35 / 5$

$\qquad \sf  \dashrightarrow \:l = 7 \: ft$

And the two rectangles are similar ~ so the ratio of their sides are equal as well ~

Assume length of greater rectangle be x

$\qquad \sf  \dashrightarrow \: (25)/(5) = (x)/(7)$

$\qquad \sf  \dashrightarrow \:x = 5 * 7$

$\qquad \sf  \dashrightarrow \:x = 35$

Now, since the length and width of the greater rectangle is known, let's find it's Area ~

$\qquad \sf  \dashrightarrow \:a = l \cdot w$

$\qquad \sf  \dashrightarrow \:a = 35 \sdot25$

$\qquad \sf  \dashrightarrow \:a = 875 \: \: ft {}^(2)$

So, Area of the greater rectangle is 875 ft²