Question

Can someone help me with this problem? Thank you!

Answer 1

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

Since, the Area of smaller rectangle is 35,

• width = 5 ft

Let's calculate it's length ~

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

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

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

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

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

Assume length of greater rectangle be x

$\qquad \sf \dashrightarrow \: \dfrac{25}{5} = \dfrac{x}{7}$

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

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

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