Question

13
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.
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Explanation:

Step1: Find the side - length of the outside square

The side - length \(s\) of the outside square is \(s=a + b\). Given \(a = 4\) units and \(b=3\) units, so \(s=4 + 3=7\) units.

Step2: Calculate the diagonal of the outside square

The formula for the diagonal \(d\) of a square with side - length \(s\) is \(d=\sqrt{2}s\). Substitute \(s = 7\) into the formula: \(d=\sqrt{2}\times7\approx7\times1.414 = 9.9\) units.

Step3: Calculate the side - length of the inside square

Use the Pythagorean theorem. The side - length \(l\) of the inside square: \(l=\sqrt{a^{2}+b^{2}}\). Substitute \(a = 4\) and \(b = 3\): \(l=\sqrt{4^{2}+3^{2}}=\sqrt{16 + 9}=\sqrt{25}=5\) units.

Step4: Calculate the diagonal of the inside square

Using the formula \(d=\sqrt{2}l\) for the diagonal of a square (where \(l\) is the side - length of the square). Substitute \(l = 5\) into the formula: \(d=\sqrt{2}\times5\approx5\times1.414 = 7.1\) units.

Answer:

The length of the diagonal of the outside square is \(9.9\) units and the length of the diagonal of the inside square is \(7.1\) units.