Question

type the correct answer in the box. in the figure, a square is inside another bigger square. if a = 4 units and b = 3 units, the length of the diagonal of the outside square rounded to the nearest tenth is units and the length of the diagonal of the inside square rounded to the nearest tenth is units.

Explanation:

Step1: Find side - length of outside square

The side - length of the outside square $s_{1}=a + b$. Given $a = 4$ units and $b = 3$ units, so $s_{1}=4 + 3=7$ units.

Step2: Calculate diagonal of outside square

The formula for the diagonal of a square is $d=\sqrt{2}s$. For the outside square with $s = 7$ units, $d_{1}=\sqrt{2}\times7\approx1.414\times7 = 9.9$ units.

Step3: Find side - length of inside square using Pythagorean theorem

For the right - triangle formed at the corner of the outside square with legs $a$ and $b$, by the Pythagorean theorem, the side - length of the inside square $s_{2}=\sqrt{a^{2}+b^{2}}$. Substituting $a = 4$ and $b = 3$, we get $s_{2}=\sqrt{4^{2}+3^{2}}=\sqrt{16 + 9}=\sqrt{25}=5$ units.

Step4: Calculate diagonal of inside square

Using the formula $d=\sqrt{2}s$ for the inside square with $s = 5$ units, $d_{2}=\sqrt{2}\times5\approx1.414\times5 = 7.1$ units.

Answer:

9.9
7.1