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 side - length $s_{1}=7$ units, the diagonal $d_{1}=\sqrt{2}s_{1}=\sqrt{2}\times7\approx7\times1.414 = 9.9$ units.

Step3: Find side - length of inside square

By the Pythagorean theorem, the side - length of the inside square $s_{2}=\sqrt{a^{2}+b^{2}}$. Substitute $a = 4$ 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 side - length $s_{2}=5$ units, the diagonal $d_{2}=\sqrt{2}s_{2}=\sqrt{2}\times5\approx5\times1.414 = 7.1$ units.

Answer:

The length of the diagonal of the outside square rounded to the nearest tenth is $9.9$ units and the length of the diagonal of the inside square rounded to the nearest tenth is $7.1$ units.