Question

Two squares are similar. Given: Square HIJK has a perimeter of 30 units and Square UVWT has a perimeter of 18 units. What is the ratio of the areas of Square HIJK to Square UVWT? 3:5 25:9 9:25 5: 3

Answer 1

If square HIJK has a perimeter of 30 units, it means that each side measures 7.5 units.

$l=\frac{30}{4}=7.5$

For the square UVWT, each side would be 4.5 units long.

$l=\frac{18}{4}=4.5$

Then, we divide these magnitudes.

$\frac{7.5}{4.5}=\frac{\frac{15}{2}}{\frac{9}{2}}=\frac{15\cdot2}{9\cdot2}=\frac{5}{3}$

Therefore, the answer is 5:3.